On the transient state probabilities for a queueing model where potential customers are discouraged by queue length

Bent Natvig

doi:10.2307/3212755

Hadidi, Nasser 1976. Appointment scheme as compared to random service and arrival times from specific distributions. Advances in Applied Probability, Vol. 8, Issue. 2, p. 250.

Bhat, U. Narayan Shalaby, Mohamed and Fischer, Martin J. 1979. Approximation techniques in the solution of queueing problems. Naval Research Logistics Quarterly, Vol. 26, Issue. 2, p. 311.

Hadidi, Nasser 1981. Queues with Partial Correlation. SIAM Journal on Applied Mathematics, Vol. 40, Issue. 3, p. 467.

Conolly, B. W. 1983. More transient results for generalised state-dependent Erlangian queues. Advances in Applied Probability, Vol. 15, Issue. 3, p. 688.

Ismail, Mourad E.H 1985. A queueing model and a set of orthogonal polynomials. Journal of Mathematical Analysis and Applications, Vol. 108, Issue. 2, p. 575.

Montazer-Haghighi, A. Medhi, J. and Mohanty, S.G. 1986. On a multiserver markovian queueing system with balking and reneging. Computers & Operations Research, Vol. 13, Issue. 4, p. 421.

Zeifman, A. I. 1991. Some estimates of the rate of convergence for birth and death processes. Journal of Applied Probability, Vol. 28, Issue. 02, p. 268.

Zeifman, A. I. 1991. Qualitative properties of inhomogeneous birth and death processes. Journal of Soviet Mathematics, Vol. 57, Issue. 4, p. 3217.

Browne, Sid and Sigman, Karl 1992. Work-modulated queues with applications to storage processes. Journal of Applied Probability, Vol. 29, Issue. 03, p. 699.

Sharma, O.P. and Maheswar, M.V.R. 1993. Transient behaviour of a simple queue with discouraged arrivals. Optimization, Vol. 27, Issue. 3, p. 283.

Granovsky, B. L. and Zeifman, A. I. 2000. Nonstationary Markovian queues. Journal of Mathematical Sciences, Vol. 99, Issue. 4, p. 1415.

Parthasarathy, P.R. and Selvaraju, N. 2001. Exact transient solution of a state-dependent queue in discrete time. Operations Research Letters, Vol. 28, Issue. 5, p. 243.

2004. Birth and Death (BDP) Process Models with Applications. American Journal of Mathematical and Management Sciences, Vol. 24, Issue. 1-2, p. 1.

Zeifman, A. I. and Satin, Ya. A. 2007. Mean characteristics of Markov queueing systems. Automation and Remote Control, Vol. 68, Issue. 9, p. 1583.

Kumar, B. Krishna Vijayakumar, A. and Sophia, S. 2008. Transient Analysis for State-Dependent Queues with Catastrophes. Stochastic Analysis and Applications, Vol. 26, Issue. 6, p. 1201.

Белорусов, Тимофей Николаевич and Belorusov, Timophey Nikolaevich 2011. Эргодичность многоканальной системы обслуживания с возможностью неприсоединения к очереди. Теория вероятностей и ее применения, Vol. 56, Issue. 1, p. 145.

Belorusov, T. N. 2012. Ergodicity of a Multichannel Queueing System with Balking. Theory of Probability & Its Applications, Vol. 56, Issue. 1, p. 120.

Ammar, S. I. El-Sherbiny, A. A. El-Shehawy, S. A. and Al-Seedy, R. O. 2012. A matrix approach for the transient solution of an M/M/1/N queue with discouraged arrivals and reneging. International Journal of Computer Mathematics, Vol. 89, Issue. 4, p. 482.

Giorno, V. Nobile, A.G. and Pirozzi, E. 2018. A state-dependent queueing system with asymptotic logarithmic distribution. Journal of Mathematical Analysis and Applications, Vol. 458, Issue. 2, p. 949.

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