In this article, we consider a compound Poisson insurance risk model with a random discount factor. This model is also known as the compound filtered Poisson model. By using some stochastic analysis techniques, a convergence result for the discounted surplus process, an expression for the ruin probability, and the upper bounds for the ruin probability are obtained.

Carousels are rotatable closed-loop storage systems for small items, where items are stored in bins along the loop. An order at a carousel consists of (say) n different items stored there. We analyze two problems: (1) minimizing the total time to fill an order (travel time) and (2) order delays as they arrive, are filled, and depart. We define clumpy orders and the nearest-end-point heuristic (NEPH) for picking them. We determine conditions for NEPH to be optimal for problem (1), and under a weak stochastic assumption, we derive the distribution of travel time. We compare NEPH with the nearest-item heuristic. Under Poisson arrivals and assumptions much weaker than in the literature, we show that problem (2) may be modeled as an M/G/1 queue.

We derive convexity results and related properties for the value functions of tandem queuing systems. The results for standard multiserver queues are new. For completeness, we also prove and generalize existing results on tandems of controllable queues. The results can be used to compare queuing systems. This is done for systems with and without batch arrivals and for systems with different numbers of on–off sources.

Compilers for ML and Haskell typically go to a good deal of trouble to arrange that multiple arguments can be passed efficiently to a procedure. For some reason, less effort seems to be invested in ensuring that multiple results can also be returned efficiently. In the context of the lazy functional language Haskell, we describe an analysis, Constructed Product Result (CPR) analysis, that determines when a function can profitably return multiple results in registers. The analysis is based only on a function's definition, and not on its uses (so separate compilation is easily supported) and the results of the analysis can be expressed by a transformation of the function definition alone. We discuss a variety of design issues that were addressed in our implementation, and give measurements of the effectiveness of our approach across a substantial benchmark set. Overall, the price/performance ratio is good: the benefits are modest in general (though occasionally dramatic), but the costs in both complexity and compile time, are low.

In this paper we develop a stochastic differential equation to describe the dynamic evolution of the congestion window size of a single TCP session over a network. The model takes into account recovery from packet losses with both fast recovery and time-outs, boundary behavior at zero and maximum window size, and slow-start after time-outs. We solve the differential equation to derive the distribution of the window size in steady state. We compare the model predictions with the output from the NS simulator.

We investigate the tail distribution of the virtual waiting times in a LRD/GI/1 queue where the arrival process is long-range dependent (LRD) and the service times are independent and identically distributed (i.i.d.) random variables. We present two lower bounds on the stationary waiting time tail asymptotics, which illustrate the different dominating components that influence server performance under various conditions. In particular, we show that the tail distribution of the stationary waiting time is bounded below by that of the associated LRD/D/1 queues resulting from replacing all random service times by the mean. This shows the performance impact purely due to the long-range dependency of the arrival process. On the other hand, when the service times are subexponential, we show that the tail distribution of the stationary waiting time is bounded below by that of the corresponding D/GI/1 queue by replacing the dependent arrival process with its associated independent version. This shows the minimum performance impact due to the tail distribution of the service times. The above two lower bounds indicate that the performance of LRD/GI/1 queues will be dominated by the heavier tail of the corresponding LRD/D/1 and D/GI/1 queues. These features are further illustrated and quantified through examples and via numerous simulation experiments.

Grammatical Framework (GF) is a special-purpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for linearizing syntax trees and parsing strings. GF can describe both formal and natural languages. The key notion of this description is a grammatical object, which is not just a string, but a record that contains all information on inflection and inherent grammatical features such as number and gender in natural languages, or precedence in formal languages. Grammatical objects have a type system, which helps to eliminate run-time errors in language processing. In the same way as a LF, GF uses dependent types in abstract syntax to express semantic conditions, such as well-typedness and proof obligations. Multilingual grammars, where one abstract syntax has many parallel concrete syntaxes, can be used for reliable and meaning-preserving translation. They can also be used in authoring systems, where syntax trees are constructed in an interactive editor similar to proof editors based on LF. While being edited, the trees can simultaneously be viewed in different languages. This paper starts with a gradual introduction to GF, going through a sequence of simpler formalisms till the full power is reached. The introduction is followed by a systematic presentation of the GF formalism and outlines of the main algorithms: partial evaluation and parser generation. The paper concludes by brief discussions of the Haskell implementation of GF, existing applications, and related work.

The question of stability for the M/G/∞ queue with gated service is investigated using a Foster–Lyapunov drift criterion. The necessary and sufficient condition for positive recurrence is shown to be the finiteness of the first moment of the service time distribution, thus weakening the stability condition given in Browne et al. [3].

The notion of the influence of a variable on a Boolean function on a product space has attracted much attention in combinatorics, computer science and other fields. Two of the basic papers dealing with this notion are by Kahn, Kalai and Linial (KKL) and Bourgain, Kahn, Kalai, Katznelson and Linial (BKKKL).

In this paper we survey the results in those papers and offer some simpler proofs, corrections, and extensions of the theorems presented there. We present several related open problems.

The aim of this paper is to prove a Turán-type theorem for random graphs. For $\gamma >0$ and graphs $G$ and $H$, write $G\to_\gamma H$ if any $\gamma$-proportion of the edges of $G$ spans at least one copy of $H$ in $G$. We show that for every graph $H$ and every fixed real $\delta>0$, almost every graph $G$ in the binomial random graph model $\cG(n,q)$, with $q=q(n)\gg((\log n)^4/n)^{1/d(H)}$, satisfies $G\to_{(\chi(H)-2)/(\chi(H)-1)+\delta}H$, where as usual $\chi(H)$ denotes the chromatic number of $H$ and $d(H)$ is the ‘degeneracy number’ of $H$.

Since $K_l$, the complete graph on $l$ vertices, is $l$-chromatic and $(l-1)$-degenerate, we infer that for every $l\geq2$ and every fixed real $\delta>0$, almost every graph $G$ in the binomial random graph model $\cG(n,q)$, with $q=q(n)\gg((\log n)^4/n)^{1/(l-1)}$, satisfies $G\to_{(l-2)/(l-1)+\delta}K_l$.

Mader asked whether every $C_4$-free graph $G$ contains a subdivision of a complete graph whose order is at least linear in the average degree of $G$. We show that there is a subdivision of a complete graph whose order is almost linear. More generally, we prove that every $K_{s,t}$-free graph of average degree $r$ contains a subdivision of a complete graph of order $r^{\frac{1}{2}{+}\frac{1}{2(s-1)}-o(1)}$.

We consider a random generalized railway defined as a random 3-regular multigraph where some vertices are regarded as switches that only allow traffic between certain pairs of attached edges. It is shown that the probability that the generalized railway is functioning is linear in the proportion of switches. Thus there is no threshold phenomenon for this property.