We consider a single server unreliable queue represented by a 2-dimensional continuous time Markov chain. At failure times, all present customers leave the system. Moreover, customers become impatient and perform synchronized abandonments, as long as the server is down. We analyze this model and derive the main performance measures using results from the basic q-hypergeometric series.

⎯We consider a single server retrial queue with batch arrivals, two phases of heterogeneous service and multiple vacations with Npolicy. The primary arrivals find the server busy or doing secondary job (vacation) will join orbit (group of repeated calls). If the number of repeated calls in orbit is less than N, the server does the secondary job repeatedly until the retrial group size reaches N....

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...

Abstract We consider an M/G/1 feedback queue with optional server vacations based on Bernoulli schedule and a single vacation policy. We assume that the server provides two types of service, type 1 with probability p1 and type 2 with probability p2 with the service times following general distribution and each arriving customer may choose either type of service. However after the completion of ...

We consider a tandem queue with two stations. The first station is an s-server queue with Poisson arrivals and exponential service times. After terminating his service in the first station, a customer enters the second station to require service at a single server, while in the meantime he is blocking his server in station 1 until he completes service in station 2, whereupon the server in stati...

We discuss how long range dependence can innuence the characteristics of a single server queue. We take the analogue of the G/M/1 queue except that the input stream is altered to exhibit long range dependence. The equilibrium queue size and equilibrium waiting time distributions each have heavy tails. By suitably selecting the parameters of the inputs, the queue size or waiting time can be made...

In this paper, we study the performance of service systems with priority upgrades. We model the service system as a single-server two-class priority queue, with queue 1 as the normal queue and queue 2 as the priority queue. The queueing model of interest has various applications in healthcare services, perishable inventory and project management. We comprehensively examine the system’s stationa...

‎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...