We consider M/G/1-type Markov chains where a transition that decreases the value of the level triggers the phase to a small subset of the phase space. We show how this structure, referred to as restricted downward transitions, can be exploited to speed-up the computation of the stationary probability vector of the chain. To this end we define a new M/G/1-type Markov chain with a smaller block s...

This paper considers a stationary single-server queue with multiple arrival streams governed by a Markov chain, where customers are served on an LCFS preemptive-resume basis. Service times of customers from each arrival stream are generally distributed and service time distributions for different arrival streams may be different. Under these assumptions, it is shown that the stationary distribu...

‎In this work‎, ‎we derive insensitive bounds for various performance measures of a single-server‎ ‎retrial queue with generally distributed inter-retrial times and Bernoulli schedule‎, ‎under the special‎ ‎assumption that only the customer at the head of the orbit queue (i.e.‎, ‎a‎ ‎FCFS discipline governing the flow from the orbit to the server) is allowed‎ ‎to occupy the server‎. ‎The method...

In this paper, we consider a BMAP/G/1 retrial queue with a server subject to breakdowns and repairs, where the life time of the server is exponential and the repair time is general. We use the supplementary variable method, which combines with the matrix-analytic method and the censoring technique, to study the system. We apply the RG-factorization of a level-dependent continuous-time Markov ch...

Consider a number of parallel queues, each with an arbitrary capacity and multiple identical exponential servers. The service discipline in each queue is firstcome-first-served (FCFS). Customers arrive according to a state-dependent Poisson process. Upon arrival, a customer joins a queue according to a state-dependent policy or leaves the system immediately if it is full. No jockeying among que...

In this paper we analyze a discrete time single server queue where the service time equals one slot The numbers of arrivals in each slot are assumed to be independent and identically distributed random variables The service process is interrupted by a semi Markov process namely in certain states the server is available for service while the server is not available in other states We analyze bot...

We consider a class of Markov chains fIn; Lng, which comprises Markov chains of the M=G=1 type and the GI=G=1 type. Here fLng is the level process and fIng the modulating process. This paper gives conditions under which (n) is an upper bound for the convergence rate to stationarity for suitable functions . Conditions for the convergence rate of E [L n ] to be o(n ) for some ; > 0 are also given...

We consider single-server queues with exponentially distributed service times, in which the arrival process is governed by a semi-Markov process (SMP). Two service disciplines, processor sharing (PS) and random service (RS), are investigated. We note that the sojourn time distribution of a type-l customer who, upon his arrival, meets k customers already present in the SMP/M/1/PS queue is identi...

This paper studies a fluid queue with coupled input and output. Flows arrive according to a Poisson process, and when n flows are present, each of them transmits traffic into the queue at a rate c/(n + 1), where the remaining c/(n + 1) is used to serve the queue. We assume exponentially distributed flow sizes, so that the queue under consideration can be regarded as a system with Markov fluid i...

In this paper, we derive the bounds formulas for the asymptotic tail distribution in a queue whose arrival process is a superposition of general periodic Markov sources. Note that we make no assumption for the structure of the general periodic Markov sources except that the underlying Markov chains are irreducible. The periodic source model in this paper is thus rather general. Taking initial s...