In this paper, we consider a discrete-time single-server queueing system with a generalized switched batch Bernoulli arrival and a general service time processes (a generalized SBBP/G/1 queue). Customers arrive to the system in batches and service times of customers are generally distributed. The batch size and the service time distributions are governed by a discrete-time alternating renewal p...

Fairness is an inherent and fundamental factor of queue service disciplines in a large variety of queueing applications. Service time variability across jobs is an important factor affecting both system performance and scheduling rules (for example, computer systems that prioritize short jobs over long jobs). Service time variability and its effects on mean response times have been studied exte...

Abstract This paper considers a FIFO single-server queue with service interruptions and multiple batch Markovian arrival streams. The server state (on and off), the type of arriving customers and their batch size are assumed to be governed by a continuous-time Markov chain with finite states. To put it more concretely, the marginal process of the server state is a phase-type alternating Markov ...

PALM-MARTINGALE CALCULUS, QUEUES WITH VACATIONS, BATCH MARKOVIAN ARRIVAL PROCESSES,SERVER SET-UP Using Palm-martingale calculus, we derive the workload characteristic function and queue length moment generating function for the BMAP IGl/1 . queue with server vacations. In the queueing system under study, the server may start a vacation at the completion of a service or at the arrival of a custo...

In this paper we report on a study of a two level preemptive priority queue with balking and reneging for lower priority level. The inter-arrival and the service times for both levels follow exponential distribution. We use a finite difference equation approach for solving the balance equations of the governing queuing model whose states are described by functions of one independent variable. H...

This paper studies two stochastic batch Markovian arrival and batch Markovian service single server queue BMAP/BMSP/1 queue Models (A) and (B) with randomly varying k* distinct environments. The arrival process of the queue has matrix representation {Dm i : 0 ≤ m ≤ M} of order ki describing the BMAP and the service process has matrix representation {Sn i : 0 ≤ n ≤ N} of order k′i describing the...

In this paper we examine a tandem network of queueing nodes where a nonstationary external Markovian arrival process feeds the initial upstream node. We develop methods for modeling the departure flow from any upstream node in its role as the arrival process to the immediate downstream node, and employ various techniques to match the interarrival moments to the downstream node to the moments of...

A sensitivity analysis of a single-server, infinite-buffer queue with correlated arrivals and correlated service times is performed. We study and compare the isolated impact of (normalized) marginal moments and (normalized) correlation structures of the arrival and service processes on the performance measures of such a queue. For these correlated processes, we use Markovian arrival processes o...