We treat a single–server vacation queue with queue–length dependent vacation schedules. This subsumes the single–server vacation queue with exhaustive service discipline and the vacation queue with Bernoulli schedule as special cases. The lengths of vacation times depend on the number of customers in the system at the beginning of a vacation. The arrival process is a batch–Markovian arrival pro...

This paper studies a batch arrival single server Bernoulli feedback queue with Poisson arrivals, two stages of heterogeneous service with different (arbitrary) service time distributions subject to random breakdowns and multiple vacations with exponential distributed with Mean vacation time . After first-stage service the server must provide the second stage service. However after the completio...

The aim of this paper is to analyze Bi-level threshold policy of M/(G1, G2)/1 with single vacation (SV) queue in a fuzzy environment. A mathematical Non linear programming (NLP) method is used to construct the membership function of the system characteristic in which the batch arrival-rate, expected group size, setup time, vacation time, service time for first essential service(FES), service ti...

 This paper deals with batch arrival unreliable queue with two phases of service and vacation under Bernoulli vacation schedule, which consist of a breakdown period and a delay period. For this model, we first derive the joint distribution of state of the server and queue size, which is one of the chief objectives of this paper. Secondly, we derive the pgf of the stationary queue size distribu...

Abstract: This paper examines the steady state behavior of an M/G/1 queue with repeated attempts in which the server may provide an additional second phase of service. This model generalizes both the classical M/G/1 retrial queue and the M/G/1 queue with classical waiting line and second optional service. We carry out an extensive stationary analysis of the system, including existence of statio...

A retrial queueing system with two types of batch arrivals, called type I and type II customers, is considered. Type I customers and type II customers arrive in batches of variable sizes according to two different Poisson processes. Service time distributions are identical and independent and are different for both types of customers. If the arriving customers are blocked due to the server bein...

Consider an M/M/1 retrial queue with collisions and working vacation interruption under N-policy. We use a quasi birth and death process to describe the considered system and derive a condition for the stability of the model. Using the matrix-analytic method, we obtain the stationary probability distribution and some performance measures. Furthermore, we prove the conditional stochastic decompo...

This paper presents the analysis of a renewal input  finite buffer queue wherein the customers can decide either to  join the queue with a probability or balk. The service process is Markovian service process ($MSP$) governed  by an underlying $m$-state Markov chain. Employing the supplementary  variable and imbedded Markov chain techniques,   the steady-state system length distributions at pre...

Two-phase M/Ek/1 queueing system with N -policy for exhaustive batch service with gating, and server startups and breakdowns is studied in this paper. The customers arrive individually according to a Poisson process and waiting customers receive batch service all at a time in the first phase and are served individually in the second phase. The server is turned off each time the system empties, ...