Daryl Daley was born in Melbourne in 1939, the son of John and Thirza Daley. John was an accountant and company administrator who became the manager of the Hotel Australia and a Melbourne City Councillor. Thirza was a talented pianist and piano teacher. Daryl had an older sister, Glyn, who was born in 1936. The siblings called each other Zip and Nip and were always friends.
When Daryl was nine, the family moved from the suburb of Coburg to Mount Ida Avenue in East Hawthorn and started to attend St John’s Camberwell Anglican Church. This ended up being something of a constant in his life: he was a parishioner at St John’s when he died. It was also at St John’s that Daryl learned to play the pipe organ, and began another of his passions, choral singing. Like his father, Daryl went to Trinity Grammar School where, remarkably, he was dux in both 1955 and 1956.
After completing his school education Daryl enrolled in a Bachelor of Science at the University of Melbourne. Daryl’s first degree was a BSc majoring in chemistry, which he completed in 1961. The following year, he completed a BA with Honours, majoring in mathematics. His Honours thesis was entitled ‘Customer impatience in single server queueing systems’.
Daryl went on to extend his Honours work in an MA under the supervision of Peter Finch. He credited Peter, then in the University of Melbourne Department of Statistics, for introducing him to a life of research. Peter gave Daryl a few of his recent publications to read, and Daryl responded by thinking about possible generalisations and extensions. Independently, Daryl found a relevant paper by the Russian author I. N. Kovalenko, which he was asked to read as part of a Science Russian subject. Putting these ingredients together led Daryl to the original ideas that he wrote up in his thesis.
In September 1962, Peter left the University of Melbourne for the Australian National University (ANU) in Canberra, and most of the subsequent contact between Daryl and Peter was by mail which, of course, in those days meant snail mail. In January 1963, the correspondence included the draft of Daryl’s MA thesis, which was submitted the following May. The thesis was examined by the famous British mathematician John Kingman who was a younger colleague of the leading British probabilist of the time, David Kendall. Kingman had visited Australia in 1963.
Early in his undergraduate years at the University of Melbourne, Daryl met Nola Hamilton who had recently moved to Melbourne from New Zealand with her family. Nola was training as a primary school teacher. They married six years later, after Daryl had finished his undergraduate degrees and won a scholarship to Cambridge. Very soon after getting married, they were on a ship to England. Their first child, John, was born in 1967, followed by their other two sons, Geoff in 1972 and Alan, in 1975.
Daryl’s MA work formed the basis of a paper, ‘General customer impatience in the queue GI/G/1’, which appeared in the second volume of The Journal of Applied Probability in 1965. It is noteworthy that this wasn’t even his first paper. In 1964, he had published a paper on single-server queues in The Journal of the Australian Mathematical Society and, with David Kendall, a paper ‘Epidemics and rumours’ in Nature. Publications in Nature were, and still are, valued as an indicator of scientific achievement at the highest level. For Daryl to have co-authored such a paper so early in his career was a considerable feather in his cap.
Daryl started a PhD at Pembroke College, Cambridge with John Kingman as his advisor, but ended up being supervised by David Kendall. He received his PhD in 1967 with a thesis entitled ‘Some aspects of Markov chains in queueing theory and epidemiology’, combining the two application areas that had motivated his research work up to that stage. The breakthrough that led to his thesis occurred in 1965 with an idea that he had after reading a paper by the University of Melbourne academic Bruce Craven in the Journal of the Australian Mathematical Society.
Further input came from a discussion with the visiting Australian Pat Moran, who was Professor of Statistics at ANU, the centre of applied probability research in Australia at the time. Daryl ended up applying his ideas to mathematical models of queues, genetic processes, and epidemics. A result of the work was the term stochastic monotonicity, which is still studied today. Very much later I can remember reading about stochastic monotonicity, but I didn’t at the time realise that the concept dated back to Daryl’s thesis.
After completing his thesis, Daryl had the opportunity to make extended academic visits to a variety of places, including Washington and Baltimore, before returning to Cambridge where he had a research fellowship at Selwyn College. Even as a young researcher, he became very much part of the applied probability community in the UK, regularly working with some well-known people.
In 1970, Daryl applied for and was offered positions in each of ANU, Monash University, and the University of Melbourne. He accepted the job at ANU because it gave him more freedom to carry out his research.
During the 1970s and ’80s, Daryl managed to find reasons to visit such destinations as Laramie (Wyoming), Bloomington (Indiana), Kalamazoo (Michigan), Chapel Hill (North Carolina), MIT Lincoln Labs (Lexington, Massachusetts), Bell Labs (New Jersey), and GTE Labs (Waltham, Massachusetts) in pursuit of his academic goals. He also extended his collaborations to Europe and Asia, with visits to Aarhus (Denmark), Stockholm (Sweden), Wroclaw (Poland), Vilnius (Lithuania), Freiburg (Germany), and Singapore. It is significant that, unlike most western academics, he spent significant time collaborating with eastern European colleagues.
In 1983, Daryl translated Comparison Methods for Queues and Other Stochastic Models, by Dietrich Stoyan, into English. In completing the translation, I believe that he made some methodological contributions. Daryl is also well known as an author of two influential books: An Introduction to the Theory of Point Processes, written with David Vere-Jones, and Epidemic Modelling: An Introduction, written with Joe Gani.
Daryl’s interest in point processes had started during his PhD studies when John Kingman pointed him to numerous references to David Vere-Jones’ work on the rate of convergence of Markov chain probabilities. This was how Daryl first heard about David Vere-Jones, with their first face-to-face meeting occurring at a meeting of the Royal Statistical Society in 1966. When Daryl returned to Cambridge in September 1968, David Kendall drew his attention to further work on point processes by Maurice Bartlett. Daryl ended up submitting a paper that extended this work. David Vere-Jones identified himself as referee of this paper and drew Daryl’s attention to his own related work.
Subsequently, David Cox asked Daryl whether he would be willing to write a survey paper on point processes as preparation for a Berkeley symposium on the subject. Daryl agreed, but suggested that David Vere-Jones should be asked to be part of the project. On the way back from Berkeley, Daryl and Nola stopped in Wellington to visit David and his wife Mary. Daryl and David ended up writing the survey paper together, by correspondence between Canberra and Wellington.
Daryl and David’s interest in point processes developed over subsequent years, culminating in the writing and publication of the first edition of An Introduction to the Theory of Point Processes in 1988. Writing the book involved many flights across the Tasman. In 2000, the publisher Springer told Daryl and David that the first edition was out of print and asked them whether they wanted to write a second edition. Initially, Daryl and David were reluctant, but Springer persisted and eventually they agreed to prepare a second edition, conditional on it being a two-volume work. This was because there was a large amount of new material that they wanted to include, and they didn’t want to delete any material from the first edition.
The preparation of Volume 1, Elementary Theory and Methods, was spread over 2000 to 2003, while Volume 2, General Theory and Structure, took longer, between 2003 and 2008. The book in both of its editions has become one of the standard references on point processes, used by researchers all over the world.
As previously noted, Daryl had been interested in modelling epidemics since his second publication with David Kendall. In 2001, Joe Gani was invited to an epidemic modelling conference at the Institute of Mathematics and Statistics in Singapore. He declined the invitation but suggested that Daryl might go in his place. At the conference, the head of the biological section of the Singapore Statistics OfficeFootnote 1 gave a talk on epidemic records.
Daryl found the data on dengue fever very interesting. This prompted him to maintain contact with the Singaporean speaker, making stopovers in Singapore on the way to three or more visits to the UK. He also chased down data on the incidence of dengue fever in Australia. In 2009, Daryl and Joe’s book Epidemic Modelling: An Introduction was published. Like An Introduction to the Theory of Point Processes, it rapidly became a standard reference in the area, introducing many researchers in public health to a stochastic approach.
It is not so well known that Daryl gave decades of behind-the-scenes service to the Statistical Society of Australia Inc (SSAI) through his contributionsFootnote 2 to the Australian Journal of Statistics/Australian and New Zealand Journal of Statistics. He was Secretary-Treasurer of the journal’s publishing company for 10 years, and then contributed as Technical Editor for 12 years. His service was recognised with his election to Honorary Life Membership of the SSAI in 1989.
In 2004, I was fortunate enough to be asked to co-edit, with Philip Pollett, a Festschrift for Daryl in the Australian and New Zealand Journal of Statistics to celebrate Daryl’s 65th birthday. I’m a little biased, but I think that the list of authors for that issue is the best that the journal has ever had, testament to the respect that these authors had for Daryl. Joe Gani’s Preface, on pages 5–11, gives an excellent account of Daryl’s life and work to 2004, with emphasis on his devoted service to the SSAI, and lists his publications to that time.
It was 1983 when Daryl first became interested in assessment of high-school students. This interest was started by a query about girls’ schools’ rankings, when the proportion of girls’ school students successfully applying to university fell from 50% to 40% as the Australian Capital Territory (ACT) Government changed from the ranking system used in NSW to a ‘new’ ACT system. Daryl organised a talk on the topic at the ACT Branch of SSAI.
With possible naivety with respect to the political debate, he offered SSAI (mostly his) help that ended up concluding that modes of assessment—multiple-choice methodology vs student-generated written responses—were the cause of bias. Daryl wrote a joint paper on the scaling of high-school marks with Eugene Seneta, which appeared in The Australian Journal of Statistics in 1985, and a number of technical reports. His conclusions were eventually written up in a report to the ACT Board of Senior Secondary Studies (BSSS) with recommendations that, in 1990, were largely adopted as standard for scaling of ACT school-based assessments. In 1995, Daryl’s report was also used by Tim Brown in advising on the scaling of ‘new’ Victorian Certificate of Education (VCE) assessments. With Bob Edwards, Daryl continued to provide advice to the BSSS and develop the system, at various times on contract or on an honorary basis. As recently as 2018, he and Bob wrote a new review that expanded on their previous work.
Possibly because he was not exposed to undergraduate students as a teaching and research academic, Daryl ended up supervising comparatively few PhD students. He was the principal supervisor for Geoff Laslett, who wrote his thesis in 1975, and Kristine Carpio, who wrote her thesis in 2006. I believe that he also helped Mark Westcott and Robin Milne substantially when they were PhD students, although he was not an official supervisor.
The Applied Probability Trust (APT) was started in 1964 by Joe Gani, just before he moved to The University of Sheffield to take up his appointment as the holder of the newly created Chair of Probability and Statistics. The APT has published The Journal of Applied Probability since 1964 and Advances in Applied Probability since 1969. These journals have grown to be amongst the most respected applied probability journals in the world. Even though the office has remained in Sheffield, Joe Gani’s eventual return to Australia has meant that there has always been significant Australian involvement in the Trust.
Joe invited Daryl to join the Trust in 1994 when a previous trustee, Ted Hannan, died. Daryl visited Sheffield every year to meet with the Executive Editor of the Trust until his health made intercontinental travel difficult in 2018. He was the Trustee who monitored the details of the operation, particularly its financial management, and made sure that nothing was missed. Daryl was also very much involved in the production of Special Issues of the APT journals, especially the Festschrifts for David Vere-Jones in 2001, Chris Heyde in 2004, and Peter Jagers in 2018. The fact that the Trust is flourishing today is due in no small measure to Daryl’s efforts.
Finally, I want to mention Daryl’s role in the Applied Probability Group at the University of Melbourne (UoM). He became an active member of this group with an honorary professorship at UoM when he and Nola moved back to Melbourne from Canberra in 2005. Three or four generations of students benefited enormously from talking with Daryl on a regular basis. Just by taking part in conversations, he exemplified the type of thinking that is characteristic of a world-class researcher. Not only did he give general advice, but he also helped in concrete ways such as by proofreading theses.
In addition to his mathematical career, Daryl was a gifted musician. He was a regular church organist at St John’s Camberwell in Melbourne, St John’s Reid in Canberra, and then again at St John’s Camberwell when he returned to live in Melbourne. He was an ever-willing accompanist, keen to contribute to musical evenings at mathematical conferences around the world. He sang with distinguished choirs while studying at Cambridge, and continued to sing all through his life with the Canberra Chorale, the Winter Singers, Oriana, the cathedral choir at St Paul’s in Melbourne, and the Melbourne Bach Choir. He was also a dextrous recorder player.
Daryl’s other great love was hiking. He was a fervent believer in the value of the after-lunch walk, and sometimes claimed that more problems were solved on walks than in seminar rooms. Wherever he travelled for mathematics, he often took the opportunity to attend local concerts and hike the local hills.
Acknowledgements
I am grateful to Daryl’s wife Nola Daley and son John Daley, and to Eugene Seneta and Nick Fisher for contributing material and for providing comments on previous versions of this text.
DARYL JOHN DALEY PUBLICATIONS
(a) Books and Monographs
A (edited with revisions). D. Stoyan, Comparison Methods for Queues and Other Stochastic Models. Wiley, Chichester, (1983) xiii + 217pp.
B (with D. Vere-Jones). An Introduction to the Theory of Point Processes. Springer-Verlag, New York, (1988) xxii + 702pp. [Out of print 1998.]
C. Determining Relative Academic Achievement for Fair Admission to Higher Education. Report to Australian National University, Canberra College of Advanced Education, and ACT Schools Authority. (1989) 149pp.
D (with J. M. Gani). Epidemic Modelling: An Introduction. Cambridge University Press, Cambridge, (1999) xii + 213pp.
E (editor). Probability, Statistics and Seismology: A Festschrift for David Vere-Jones (Journal of Applied Probability 38A), (2001) xvii +292pp.
F (with D. Vere-Jones). An Introduction to the Theory of Point Processes, 2nd edition. Springer- Verlag, New York. Volume I: Elementary Theory and Methods (2003), xxii + 469pp. Volume II: General Theory and Structure (2008), xvii + 573pp.
G. Re-typeset TEX version (with minor editing) of Bochner, S. and Chadrasekharan, K. (1949), Fourier Transforms, Princeton University Press, iv + 128pp (typewritten original vi + 222pp).
H (with R.A. Edwards). Revisiting How ACT ATARs are Determined. Report to ACT BSSS and UAC Sydney.
(b) Articles in Journals &c.
1. Single-server queueing systems with uniformly limited queueing time. J. Aust. Math. Soc. 4 (1964) 489–505.
2 (with D. G. Kendall). Epidemics and rumours. Nature 204 (1964) 1118.
3. General customer impatience in the queue GI/G/1. J. Appl. Probab. 2 (1965) 186–205.
4. On a class of renewal functions. Proc. Camb. Philos. Soc. 61 (1965) 519–526.
5 (with D. G. Kendall). Stochastic rumours. J. Inst. Math. Appl. 1 (1965) 42–55.
6. Concerning the spread of news in a population of individuals who never forget. Bull. Math. Biophys. 29 (1967) 373–376.
7 (with P. A. P. Moran). Two-sided inequalities for waiting time and queue size distributions in GI/G/1. Teor. Veroyat. 13 (1968) 356–359.
8. The serial correlation coefficients of waiting times in a stationary single server queue. J. Aust. Math. Soc. 8 (1968) 683–699.
9. The correlation structure of the output process of some single server queueing systems. Ann. Math. Statist. 39 (1968) 1007–1019.
10. Extinction conditions for certain bisexual Galton–Watson branching processes. Z. Wahrs. 9 (1968) 315–322.
11. Monte Carlo estimation of the mean queue size in a stationary GI/M/1 queue. Operat. Res. 16 (1968) 1002–1005.
12. Stochastically monotone Markov chains. Z. Wahrs. 10 (1968) 305–317.
13. Quasi-stationary behaviour of a left-continuous random walk. Ann. Math. Statist. 40 (1969) 532–539.
14. Extinction probabilities in a branching process: a note on Holgate and Lakhanie’s paper. Bull. Math. Biophys. 31 (1969) 35–37.
15. Total waiting time in a busy period of a stable single server queue. J. Appl. Probab. 6 (1969) 550–564.
16 (with D. R. Jacobs, Jr.). (as 15), II. J. Appl. Probab. 6 (1969) 565–572.
17. Integral representations of transition probabilities and serial covariances of certain Markov chains. J. Appl. Probab. 6 (1969) 648–659.
18. Spectral properties of weakly stationary point processes. Bull. Internat. Statist. Inst. 43 (1969) Bk. 2 319–321.
19. The non-existence of stationary infinite Newtonian universes and a multi-dimensional model of shot noise. Nature 227 (1970) 935.
20. Weakly stationary point processes and random measures. J. Roy. Statist. Soc. Ser. B 33 (1971) 406–428.
21. The definition of a multi-dimensional generalization of shot noise. J. Appl. Probab. 8 (1971) 128–135.
22. Asymptotic properties of stationary point processes with generalized clusters. Z. Wahrs. 21 (1972) 65–76.
23 (with D. Vere-Jones). A summary of the theory of point processes. In Stochastic Point Processes (ed. P. A. W. Lewis) Wiley, New York (1972) 299–383.
24. A bivariate Poisson queueing process that is not infinitely divisible. Proc. Camb. Philos. Soc. 72 (1972) 449–450.
25. Various concepts of orderliness for point processes. In Stochastic Geometry (ed. E. F. Harding & D. G. Kendall) Wiley, Chichester (1973) 148–161.
26. Poisson and alternating renewal processes with superposition a renewal process. Math. Nachr. 57 (1973) 359–369.
27. Markovian processes whose jump epochs constitute a renewal process. Quart. J. Math. Oxford Second Ser. 24 (1973) 97–105.
28 (with R. K. Milne). The theory of point processes: a bibliography. Internat. Statist. Review 41 (1973) 183–201.
29 (with D. Oakes). Random walk point processes. Z. Wahrs. 30 (1974) 1–16.
30. Characterizing pure loss GI/G/1 queues with renewal output. Proc. Camb. Philos. Soc. 75 (1974) 103–107.
31. Notes on queueing output processes. In Mathematical Methods in Queueing Theory (ed. A. B. Clarke) Springer-Verlag (Lect. Notes Econ. and Math. Systems 98) (1974) 351–358.
32. Computation of bi- and tri-variate normal integrals. Appl. Statist. 23 (1974) 435–438.
33. Further second-order properties of the output process of certain single-server queues. Stoch. Proc. Appl. 3 (1975) 185–191.
34 (with D. N. Shanbhag). Independent inter-departure times in M/G/1/N queues. J. Roy. Statist. Soc. Ser. B 37 (1975) 259–263.
35 (with R. K. Milne). Orderliness, intensities, and Palm–Khinchin equations for multivariate point processes. J. Appl. Probab. 12 (1975) 383–389.
36. Certain bounds concerning characteristic functions. Aust. J. Statist. 17 (1975) 91–93.
37. The deterministic version of a stochastic model: what is it, and what is its use? Proc. 1975 Summer Res. Inst. Aust. Math. Soc.
38 (with R. S. Anderssen, R. P. Brent, & P. A. P. Moran). Concerning
$\int_0^1 \cdot \cdot \cdot \int_0^1 {(x_1^2 + \cdot \cdot \cdot + x_k^2)^{1/2}}d{x_1}\,\, \cdot \cdot \cdot d{x_k}$ and a Taylor series method. SIAM J. Appl. Math. 30 (1976) 22–30.38a. Solution to SIAM Problem 75-12, An Average Distance. SIAM Review 18 (1976) 498–499.
39. Another upper bound for the renewal function. Ann. Probab. 4 (1976) 109–114.
40. Queueing output processes. Adv. Appl. Probab. 8 (1976) 395–415.
41. Tighter bounds for the absolute third moment. Scand. J. Statist. 4 (1977) 183–184.
42. Inequalities for moments of tails of random variables, with a queueing application. Z. Wahrs. 41 (1977) 139–143.
43. Upper bounds for the renewal function via Fourier methods. Ann. Probab. 6 (1978) 876–884.
44 (with N. R. Mohan). Asymptotic behaviour of higher order moments of renewal processes and random walks. Ann. Probab. 6 (1978) 516–521.
45. Bounds for the variance of certain stationary point processes. Stoch. Proc. Appl. 7 (1978) 255–264.
46 (with R. Bergmann, T. Rolski, & D. Stoyan). Bounds for cumulants of waiting times in GI/GI/1 queues. Math. Operat.-forsch. Statist. Ser. Optim. 9 (1978) 257–263.
47. Return probabilities for certain three dimensional random walks. J. Appl. Probab. 16 (1979) 45–53.
48. Bias in estimating the Malthusian parameter for Leslie matrices. Theor. Popul. Biol. 15 (1979) 257–263.
49. Lattice-valued random walks with Markov chain dependent steps. Math. Proc. Camb. Philos. Soc. 86 (1979) 115–126.
50. Markov chains and a pecking order problem. In Interactive Statistics — Proc. Applied Statistics Conference, Sydney, 1979 (ed. D. R. McNeil) North-Holland, 247–254.
51 (with M. S. Boyce). Population tracking of fluctuating environments and natural selection for tracking ability. Amer. Naturalist. 115 (1980) 480–491.
52. Tight bounds for the renewal function of a random walk. Ann. Probab. 8 (1980) 615–621.
53. A note on bounds for the supremum metric for discrete random variables. Math. Nachr. 99 (1980) 939–947.
54 (with P. Narayan). Series expansions of probability generating functions and bounds for the extinction probability of a branching process. J. Appl. Prob. 17 (1980) 939–947.
55 (with G. D. Clark-Walker & C. R. McArthur). Does mitochandrial DNA length influence the frequency of spontaneous petite mutants in yeasts? Current Genetics 4 (1981) 7–12.
56. Aufgabe 862, 862A Elemente der Math. 36 (1981) 67–68.
57. The absolute convergence of weighted sums of dependent sequences of random variables. Z. Wahrs. 58 (1981) 199–203.
58 (with J. Haslett). A thermal energy storage process with controlled input. Adv. Appl. Probab. 14 (1982) 257–271.
59. Stationary point processes with Markov-dependent intervals and infinite intensity. J. Appl. Prob. 19A (1982) 313–320.
60. Infinite intensity mixtures of point processes. Math. Proc. Camb. Philos. Soc. 92 (1982) 109–114.
61 (with P. G. Hall & C. C. Heyde). Further results on the survival of a gene represented in a founder population. J. Math. Biol. 14 (1982) 355–363.
62. Solution of Advanced Problem 6062*: nesting regular n-gons. Amer. Math. Monthly 89 (1982) 503.
63 (with Mark Boyce). Some consequences of seasonality in population models. In Mathematical Models of Renewable Resources (ed. Roland Lamberson) Humboldt State Univ. Mathematical Modelling Group (1983) 99–102.
64. Optimally nested regular N -gons. J. Optim. Theory Appl. 41 (1983) 425–437.
65 (with T. Rolski). A light traffic approximation for a single-server queue. Math. Operat. Res. 9 (1984) 624–628.
66 (with P. G. Hall). Limit laws for the maximum of weighted and shifted i.i.d. random variables. Ann. Probab. 12 (1984) 571–587.
67 (with T. Rolski). Some comparability results for waiting time in single- and many-server queues. J. Appl. Probab. 21 (1984) 887–900.
68. Measuring the avoidance of super-parasitism: are balls scattered non-randomly into boxes? In Data: A Collection of Problems from Many Fields for the Student and Research Worker (ed. D. F. Andrews & A. M. Herzberg) Springer-Verlag, New York, (1985) 299–300.
69. Pecking Order Problem. In Encyclopedia of Statistical Sciences (ed. S. Kotz & N. L. Johnson) John Wiley, New York 6 (1985) 659–660.
70. What is a two-sex population process? Adv. Appl. Probab. 17 (1985) 230.
71. Standardization by bivariate adjustment of internal assessments: sex bias and other statistical matters. Aust. J. Educ. (1985) 231–247.
72. Making Year 12 marks equitable in the ACT: sex bias in ASAT? PACT J. 3 (2) (1985) 12–19.
73. How should NSW HSC examination marks be reported? Independent Education 5 (2) (1985) 34–38.
74. Submission to Senate Standing Committee on Education and the Arts. Official Hansard Report, Monday 13 May 1985, 60–68.
75. Supplementary Submission to Senate Standing Committee on Education and the Arts, September 1985.
76. A lower bound for mean characteristics in Ek/G/1 and GI/Ek/1 queues. Math. Operat.-forsch. Statist., Ser. Optim. 17 (1986) 117–124.
77 (with E. Seneta). Modelling examination marks. Aust. J. Statist. 28 (1986) 143–153.
78 (with D. M. Hull & J. M. Taylor). Bisexual Galton–Watson branching processes with superadditive mating functions. J. Appl. Probab. 23 (1986) 585–600.
79. Certain optimality properties of the first-come first-served discipline for G/G/s queues. Stoch. Proc. Appl. 25 (1987) 301–308.
80 (with A. Eyland). The new and old HSC: figures, facts and fantasies. Independent Education 17 (3) (1987) 22–25.
81 (with D. Vere-Jones). Extended probability generating functional with application to mixing properties of cluster point processes. Math. Nachr. 131 (1987) 311–319.
82 (with M. R. Chernick & R. P. Littlejohn). A time-reversibility relationship between two Markov chains with exponential stationary distributions. J. Appl. Probab. 25 (1988) 418–422.
83. Tight bounds on the exponential approximation of some aging distributions. Ann. Probab. 16 (1988) 414–423.
84 (with J. Maindonald). A unified view of models describing the avoidance of superparasitism. IMA J. Math. Applied in Med. Biol. 6 (1989) 161–178.
85 (with J. M. Gani & D. A. Ratkowsky). Markov chain models for type–token relationships. In Statistical Inference in Stochastic Processes (ed. N. U. Prabhu & I. V. Basawa) Marcel Dekker, New York (1991) 209–232.
86 (with T. Rolski). Light traffic approximations in queues. Math. Operat. Res. 16 (1991) 57–71.
87. Ranking in a one-factor model used to describe examination marks. In The Frontiers of Modern Statistical Inference Procedures, II (Proc. and Discussion of the Second International Conference on Inference Procedures associated with Statistical Ranking and Selection, ed. E. Bofinger et al.), Amer. Sciences Press, Columbus OH, (1992) pp.381–396.
88. Discussion of Sobel’s paper “New formulation for normal selection”. In The Frontiers of Modern Statistical Inference Procedures, II (ed. E. Bofinger et al.), Amer. Sciences Press, Columbus OH, (1992), pp.375–378.
89 (with T. Rolski). Light traffic approximations in many-server queues. Adv. Appl. Probab. 24 (1992) 202–218.
90 (with T. Rolski). Finiteness of waiting-time moments in general stationary single-server queues. Ann. Appl. Probab. 2 (1992) 987–1008.
91 (with L. D. Servi). Exploiting Markov chains to infer queue-length from transactional data. J. Appl. Probab. 29 (1992) 713–732.
92 (with A. Ya. Kreinin & C. D. Trengove). Bounds for mean waiting times in single-server queues: a survey. In Queueing and Related Models (eds. U. N. Bhat & I. V. Basawa), Clarendon Press, Oxford, (1992) pp.177–223.
93 (with L. D. Servi). A two-point Markov chain boundary value problem. Adv. Appl. Probab. 25 (1993) 607–630.
94 (with J. Gani). A random allocation model for carrier-borne epidemics. J. Appl. Probab. 30 (1993) 751-765.
95 (with T. Rolski). Light traffic approximations in general stationary single-server queues. Stoch. Proc. Appl. 49 (1994) 141–158.
96 (with L. D. Servi). Approximating last exit probabilities of a random walk, with application to conditional queue length moments within busy periods of M/GI/1 queues. J. Appl. Probab. 31A (1994) 251–267.
97 (with J. Gani). A deterministic general epidemic model in a stratified population. In Probability, Statistics and Optimization: A Tribute to Peter Whittle (ed. F.P. Kelly), Chichester, Wiley, (1994) pp.117–132.
98 (with R. Foley & T. Rolski). Conditions for finite moments of waiting times in G/G/1 queues. Queueing Systems 17 (1994) 89–106.
99 (with L. D. Servi). A further study of an approximation for last-exit probabilities of a random walk. J. Appl. Math. Stoch. Anal. 7 (1994) 411–422.
100 (with C. Stricker & S. J. Redman). Statistical analysis of synaptic transmission: model discrimination and confidence limits. Biophys. J. 67 (1994) 532–547.
101. Epidemics. In Climate Impact Assessment Methods for Asia and the Pacific (Proc. Regional Symposium for Australian International Development Assistance Bureau, Canberra 10– 12 March, 1993), ed. A. J. Jakeman & A. B. Pittock, AIDAB Canberra (1994) pp.145–148.
102. Two-moment scaling formulae for aggregating examination marks. Aust. J. Statist. 37 (1995) 253–272.
103 (with R. Foley & T. Rolski). A note on convergence rates in the strong law for strong mixing sequences. Probab. Math. Statist. 16 (1996) 19–28.
104 (with L. D. Servi). Estimating waiting times from transactional data. OR J. Computing 9 (1997) 224–229.
105. Some results for the mean waiting-time and work-load in GI/GI/k queues. In Frontiers in Queueing Systems: Models and Applications in Science and Engineering, (ed. J. H. Dshalalow), CRC Press, Boca Raton FA, (1997) pp.35–59.
106 (with R. Vesilo). Long range dependence of point processes, with queueing examples. Stoch. Proc. Appl. 70 (1997) 265–282.
107 (with J. Gani). Some control methods for epidemics. In Advances in the Theory and Practice of Statistics: A Volume in Honor of Samuel Kotz (ed. N. L. Johnson and N. Balakrishnan), John Wiley & Sons, (1997) 125–142.
108 (with L. D. Servi). Idle and busy periods in stable M/M/k queues. J. Appl. Probab. 35 (1998) 950–962.
109. Contribution to the Discussion of Anderson and Catchpole’s ‘Comparing performance of NSW and Victorian students in a first-year mathematics course. Australian & New Zealand J. Statist. 40 (1998) 399–400.
110 (with L. D. Servi). Moment estimation of customer loss rates from transactional data. J. Appl. Math. Stoch. Anal. 11 (1998) 301–310.
111 (with L. D. Servi). Estimating customer loss rates from transactional data. In Applied Probability and Stochastic Processes: A Festschrift for Julian Keilson (ed. J. G. Shantikumar and U. Sumita), Kluwer Publishers, (1999) 313–332.
112 (with J. Gani). Models for the spread of infection via pairing at parties. In Applied Probability and Stochastic Processes: A Festschrift for Julian Keilson (ed. J. G. Shantikumar and U. Sumita), Kluwer Publishers, (1999) 95–113.
113 (with H. Stoyan and D. Stoyan). The volume fraction of a Poisson germ model with maximally non-overlapping spherical grains. Adv. Appl. Probab. 31 (1999) 610–624.
114. The Hurst index of long-range dependent renewal processes. Ann. Probab. 27 (1999) 2035–2041.
115 (with J. M. Gani and S. Yakowitz). An epidemic with individual infectivities and susceptibilities. Math. Computer Modelling 32 (2000) 155–167.
116 (with C. L. Mallows and L. R. Shepp). A one-dimensional Poisson growth model with non- overlapping intervals. Stoch. Proc. Applic. 90 (2000) 223–241.
117 (with R. Vesilo). Long-range dependence of inputs and outputs of classical queues. In Analysis of Communication Networks: Call Centres, Traffic and Performance, D. R. McDonald and S. R. E. Turner (eds), (Fields Institute Communications 28) (2000) 179–186.
118 (with T. Rolski and R. Vesilo). Long-range dependent point processes and their Palm–Khinchin distributions. Adv. Appl. Probab. 34 (2000) 1051–1063.
119. The busy period of the M/G/∞ queue. Queueing Systems 38 (2001) 195–204.
120. The moment index of minima. J. Appl. Probab. 38A (2001) 33–36.
121 (with L. D. Servi). Loss probabilities of hand-in traffic under various protocols, I: Models and algebraic results. Telecommun. Systems 19 (2002) 209–226.
122 (with L. D. Servi). Loss probabilities of hand-off traffic under various protocols, II: Model comparisons. Performance Evaluation 55 (2004) 231–249.
123 (with D. Vere-Jones). Scoring probability forecasts for point processes: The entropy score and information gain. J. Appl. Probab. 42A (2004) 297–312.
124 (with A. Baltru¯nas and C. Klüppelberg). Tail behaviour of the busy period of a GI/G/1 queue with subexponential service times. Stoch. Proc. Appl. 111 (2004) 237–258.
125. Further results for the lilypond model. In Spatial Point Process Modelling and its Applications/International Conference on Spatial Point Process Modelling and its Applications (SPPA) (eds. Adrian Baddeley, Pablo Gregori, Jorge Mateu, Radu Stoica and Dietrich Stoyan), Publ. Universitat Jaume I, Castelló de la Plana, (2004) 55–65.
126 (with M. S. Boyce and Cailin Xu). Harvesting in seasonal environments. J. Math. Biol. 50 (2005), 663–682.
127 (with G. Last). Descending chains, the lilypond model, and mutual nearest-neighbour matching. Adv. Appl. Probab. 37 (2005) 604–628.
128 (with F. Ballani and D. Stoyan). Modelling the microstructure of concrete with spherical grains. Comput. Materials Sci. 35 (2006) 399–407.
129 (with C. M. Goldie). The moment index of minima (II). Statist. Probab. Letters 76 (2006) 831–837.
130. Relating ACT and NSW UAI populations via PISA and other scores. Report to ACT Board of Senior Secondary Studies and NSW University Admissions Committee. (2006), 11pp.
131 (with Long-Thang Lo and Z.H. Sturchowski). On the definition of an amorphous solid of uniform hard spheres. Solid State Sci. 8 (2006) 868–879.
132 (with Edward Omey and Rein Vesilo). The tail behaviour of a random sum of subexponentially distributed random variables and vectors. Extremes 10 (2007) 21–39.
133 (with K.J.E. Carpio). Long-range dependence of Markov chains in discrete time on countable state space. J. Appl. Probab. 44 (2007) 1047–1055.
134 (with T. Rolski and R. Vesilo). Long-range dependence in a Cox process directed by a Markov renewal process. J. Appl. Math. Decision Sci. (2007), Article ID 83852, 15 pp., doi:10.1155/2007/83852.
135 (with D. Vere-Jones). David George Kendall and Applied Probability. J. Appl. Probab. 45 (2008), 293–296.
136. David George Kendall: Some Personal Reminiscences. Extract in Churchill Review, 45 (2008), 85, Churchill College, Cambridge.
137. Long-range dependence in a Cox process directed by an alternating renewal process. In Probability and Mathematical Genetics, London Mathematical Society Lecture Notes series 378 (2010), N.H. Bingham and C.M. Goldie (eds), pp.169–184.
138. Comment on the paper by Gani. Australian New Zealand J. Statist. 52 (2010), 330–334.
139 (with W.S. Kendall, Ilya Molchanov and Eva Vedel Jensen) Dietrich Stoyan: A Tribute on the occasion of his Seventieth Birthday. Adv. Appl. Probab. 42 (3) (2010), i–1v.
140 (with R.J. Swift). The size of a major epidemic of a vector-borne disease. J. Applied Probab. 48A (2011) 235–247.
141 (with C. Klüppelberg and Y. Yang). Corrigendum to “Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times”. Stoch. Proc. Appl. 139 (2011), 2186–2187.
142. Revisiting queueing output processes: a point process viewpoint. Queueing Systems and their Applications 68 (2011), 395–405. DOI: 10.1007/s11134-011-9232-3.
143 (with E. Porcu, M. Bevilacqua, M. Buhmann). Radial basis functions with compact support for multivariate geostatistics. Stochastic Environmental Research and Risk Assessment 27, (2013), 909–922.
144 (with E. Porcu). Dimension walks and Schoenberg spectral measures. Proc. Amer. Math. Soc. 142 (2014) 1813–1824.
145 (with S. Ebert and R.J. Swift). Size distributions in random triangles. J. Appl. Probab. 51A, (2014) 283–295.
146 (with Y. Nazarathy and J.S.H. van Leeuwaarden). BRAVO for many-server QED systems with finite buffers. Adv. Appl. Probab. 47 (2015) 231–250.
147 (with E. Porcu and M. Bevilacqua). Classes of compactly supported covariance functions for multivariate random fields. Stochastic Environmental Research and Risk Assessment 29 (2015) 1249–1263.
148 (revision of J. Gani original article). Stochastic epidemic models. Wiley StatsOnline reference (2015).
149 (with S. Ebert and G. Last). Two lilypond systems of finite line segments. Probab. Math. Statist., Wrocław FIND PUBL. co-ords.
150 (with Y. Nazarathy and J.S.H. van Leeuwaarden). The asymptotic variance of thinned counts in birth–death processes (in preparation).
151 (with Y. Nazarathy). BRAVO in M/M/s/K with reneging. (in preparation).
152 (with M. Brown). The Wasserstein and sup metrics for distributions close to the exponential: some tight inequalities. (in preparation).
153. Joseph Mark Gani (obituary), Gaz. Australian Math. Soc. (to appear).
154. Renewal function asymptotics refined ´a la Feller. Probab. Math. Statist., Wroclaw (to appear).
(b′) Other Manuscripts: Incomplete and/or in preparation for publication
136. The many-server queue and the ‘essential lemma’ of Kiefer and Wolfowitz.
137 (with P. M. Glynn). Estimation of the lifetime distribution of a renewal process from backward recurrence times: when non-parametric maximum likelihood estimation fails.
138 (with L. D. Servi). Identifying nodes from multi-fingered probes: decoding a noisy bit-stream from single- and multiple-check information.
139 (with L. D. Servi). An M/M/k vacation model and the cost of exploiting its idle time.
140 (with V. Isham). Structured Reed–Frost models to describe an epidemic lasting over an extended period.
141. Packings and approximate packings of spheres (II): Simulation using the lilypond growth protocol.
142 (with P. M. Glynn). The output process of an M/M/k queue with simple balking.
143 (with L. D. Servi). Quality of service measures for mixed voice and data traffic.
144. A simulation study of some aspects of scaling exam. marks.
145 (with F. Ball and J. M. Gani). An S–I–R epidemic model with a continuum of types of susceptibles and infectives.
146 (with L. D. Servi). Likelihood estimation of balking and reneging rates from transactional data.
147 (with L. D. Servi). Managing a many-server facility subject to regulatory control on the quality of service.
148 (with L. D. Servi). A survey concerning estimation and other problems for transactional data.
149 (with N. J. Duffield). Bounds on buffer content in a fluid flow model.
150 (with V. Kalashnikov). Approximations for buffer content in a fluid flow model.
151 (with T. J. Ott). On a fluid flow model for a packet switch.
152. Busy probabilities of stationary M/M/k queues.
153. Bias in percentile-based observed score equating.
154. A model for finite line-segments from the lilypond protocol.
155 (with O. Nerman). Branching processes in finite populations and certain random directed graphs.
156. A partial credit model for ranking.
157. Infectious contacts in S-I-R epidemic and endemic models.
158. Modelling dengue seroprevalence in Singapore, 1970–2008.
(c) Reports and Technical Reports (not otherwise published)
R1. Some problems in the theory of point processes. Inst. Statistics Univ. N. Carolina at Chapel Hill, Mimeo Series #772. (1971) 14pp.
R2. The closeness of uniform random points in a square and a circle. Dept. Statistics Univ. N. Carolina Chapel Hill, Mimeo Series #1327 (1981) 7pp.
R3. Distances of random variables and point processes. Dept. Statistics Univ. N. Carolina Chapel Hill, Mimeo Series #1331 (1981) 22pp.
R4. Producing consistent Tertiary Entrance Scores in the ACT. Distributed by ACT Schools Accrediting Agency (1984) 20pp.
R5. Different sex differences from different modes of assessment: common experiences in three countries. Supplement to report to committee preparing Making Admission to Higher Education Fairer (1986), 26pp. (Included at Appendix 2 of [C, 1989].)
R6. Scaling NSW HSC marks for school-leaver admission. Canberra College of Advanced Education (1987) 56pp.
R7. Modelling examination marks II. Dept. Statistics, Univ. N. Carolina, Mimeo Series #1745 (1987).
R8. 1985 results in Law at ANU: A preliminary predictive validity study of ACT TE scores and NSW HSC aggregates as selection critria. Faculty of Law, ANU (1987).
R9. The existence of sex bias in ACT tertiary entrance scores. Canberra Statist. Tech. Rep. 009–90.
R10 (with R. B. Mitchell). Report on the Existence of Gender-linked Bias in ACT Tertiary Entrance Scores. ACT Schools Accrediting Agency etc. February 1990.
R11. The nature of TE score data. Invited paper prepared for conference “Use of Year 12 Assessment Data for Tertiary Entrance,” Sydney, 10–11 October 1994.
R12. Some statistical properties of link travel times. National Institute of Statistical Science, Research Triangle Park NC, Tech. Rep. June, 1996.
R13. Packings and approximate packings of spheres. National Institute of Statistical Science, Research Triangle Park NC, Tech. Rep. March, 2000.
R14. Two-sided exponential distribution for ‘error’. Draft for National Institute of Statistical Science, Research Triangle Park NC, Tech. Rep.
R15. Relating ACT and NSW UAI populations via PISA and other scores. Report to ACT Board of Senior Secondary Studies, December 2006. 11pp. [available on ACT BSSS website.]
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