In this paper we generalize the martingale of Kella and Whitt to setting Lévy-type processes show that (local) martingales obtained are in fact square-integrable which upon dividing by time index converge zero almost surely L 2 . The reflected process is considered as an example.

This paper considers the problem of obtaining approximate expressions for first moment W Gs stationary waiting time distribution in an M/G/s queueing system. Special attention is paid to case G ≡ D, i.e., constant service times. Most known approximations are fact heavy traffic which have rather large relative errors light case. In present study both and behavior (W Ds ) taken into account. order obtain mean it appears be useful introduce a quantity (the “normed cooperation coefficient”)...

Single-served, multiqueue systems with cyclic service in discrete time are considered. Nonzero switchover times between consecutive queues assumed; the strategies at various may differ. A decomposition for amount of work such is obtained, leading to an exact expression a weighted sum mean waiting queues.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper gives an overview of recent research on the impact scheduling tail behavior response time a job. We cover preemptive and non-preemptive disciplines, consider light-tailed heavy-tailed distributions, discuss optimality properties. The focus is results, intuition insight rather than methods techniques.

This paper is devoted to the practical implications of theoretical results obtained in Part I [1] for queueing systems consisting two single-server queues series which service times an arbitrary customer at both are identical. For this purpose some tables and graphs included. A comparison made—mainly by numerical asymptotic techniques—between following phenomena: (i) behaviour second counter two-stage tandem queue (ii) a with same offered (Poisson) traffic as first service-time distribution...

This paper considers a queueing system consisting of two single-server queues in series, which the service times an arbitrary customer at both are identical. Customers arrive first queue according to Poisson process. Of this model, is importance modern network design, rather complete analysis will be given. The results include necessary and sufficient conditions for stationarity tandem system, expressions joint stationary distributions actual waiting virtual queues, explicit (i.e., not...

In this paper we propose a prototype model for the problem of managing waiting lists organ transplantations. Our captures double-queue nature problem: there is queue patients, but also organs. Both may suffer from “impatience”: health patient deteriorate, and organs cannot be preserved longer than certain amount time. Using advanced tools queueing theory, derive explicit results key performance criteria: rate unsatisfied demands outdatings, steady-state distribution number on shelf, time...

Abstract In this paper we study the number of customers in infinite-server queues with a self-exciting (Hawkes) arrival process. Initially assume that service requirements are exponentially distributed and Hawkes process is Markovian nature. We obtain system differential equations characterizes joint distribution intensity customers. Moreover, provide recursive procedure explicitly identifies (transient stationary) moments. Subsequently, allow for non-Markovian processes nonexponential...

We consider a L\'evy process reflected at the origin with additional i.i.d. collapses that occur Poisson epochs, where collapse is jump downward to state which random fraction of just before jump. first study general case, then specialize case spectrally positive and finally we further two cases Brownian motion compound exponential jumps minus linear slope.

We consider an M/G/1 queue with the special feature of additional negative customers, who arrive according to a Poisson process. Negative customers require no service, but at their arrival stochastic amount work is instantaneously removed from system. show that workload distribution in this equals waiting time GI/G/1 ordinary only; effect incorporated new