We consider a single server queue in discrete time, in which customers must be served before some limit sojourn time of geometrical distribution. A customer who is not served before this limit leaves the system. The fact of serving customers, holding them in queue or losing them induce costs. The purpose is to decide when to serve the customers so as to minimize these costs. We use a Markov Dec...

This paper treats a discrete-time finite buffer batch arrival queue with a single working vacation and partial batch rejection in which the inter-arrival and service times are, respectively, arbitrary and geometrically distributed. The queue is analyzed by using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at prearrival,...

We consider the buffer content of a fluid queue or storage process. The buffer content varies in a way that depends on the state of an underlying three-state Markov process. In state 0 the buffer content increases at a rate α(x) that is a function of the current buffer level x; in states 1 and 2 it decreases linearly, with different speeds. We study the steady-state buffer content, by using lev...

This paper studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. Scaling the arrival rates λi by a factor N and the rate qij of the background process by a factor N, with α ∈ R, we establish a central limit theorem as N tends to ∞. We find different scaling regime...

In this work, we propose a new model of the Downlink Shared Channel (DSCH) buffer in UMTS Release ’99 cellular systems. Under our assumptions, the available bandwidth dedicated to DSCH traffic is limited by voice connections carried by Dedicated Channels (DCHs) on the one hand, and by traffic on the Forward Access Channel (FACH) on the other hand. We propose to model the DSCH buffer content as ...

This paper studies a queueing model with the finite buffer of capacity K in wireless cellular networks, which has two types of arriving calls—handoff and originating calls, both of which follow the Markov arriving process with different rates. The channel holding times of the two types of calls follow different phase-type distributions. Firstly, the joint distribution of two queue lengths is de...

Consider an M/G/c queue with homogeneous servers and service time distribution F . It is shown that an approximation of the service time distribution F by stochastically smaller distributions, say Fn, leads to an approximation of the stationary distribution π of the original M/G/c queue by the stationary distributions πn of the M/G/c queues with service time distributions Fn. Here all approxima...

We consider an M/G/1 queue with general retrial times where the blocked customers may balk the system, or join the priority queue, or enter the orbit. As soon as a customer is served, he will decide either to leave the system or join the orbit for another service in accordance with an FCFS discipline. We assume that only the customer at the head of the orbit is allowed to retry for service. We ...

This paper investigates a discrete-time system with Markov modulated batch Bernoulli process (MMBP) inputs, general service times, and a finite capacity waiting room (queue). The FIFa and space priority service rules are considered. The main motivation for studying this type of queue is its potential applicability to time-slotted communication systems in broadband ISDN (B-ISDN). Applying the su...