Analysis of a M^X/G(a,b)/1 queueing system with vacation interruption

Abstract

In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least 'a' customers waiting for service say ξ, he serves a batch of min (ξ, b) customers, where b ≥ a. On the other hand, if the queue length is at the most 'a-1', the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary job is interrupted abruptly and the server resumes for primary service, if the queue size reaches 'a', during the secondary job period. On completion of the secondary job, the server remains in the system (dormant period) until the queue length reaches 'a'. For the proposed model, the probability generating function of the steady state queue size distribution at an arbitrary time is obtained. Various performance measures are derived. A cost model for the queueing system is also developed. To optimize the cost, a numerical illustration is provided.

Performance analysis of single server non-Markovian retrial queue with working vacation and constant retrial policy

“…On using the condition lim z→1 P (z) = 1 in equation (19) we derive the steady state condition as γ > λ 2 μ b −λ (which coincides with the stability condition given by Tien Van Do [24])…”

“…• Substituting in (19), the PGF of the retrial queue size distribution for single server retrial queue with working vacation and constant retrial policy is obtained.…”

“…Arumuganathan et al [18] analyzed a steady state non-Markovian bulk queueing system with N-policy and different types of vacation. Haridass and Arumuganathan [19] analyzed a batch arrival, bulk service queueing system with interrupted vacation.…”

Study on Infinite Buffer Batch Size Dependent Bulk Service Queue with Queue Length Dependent Vacation

“…Batch service queues with SV where the behavior of the system analyzed by the supplementary variable technique (SVT), can be found in [ 12 , 13 , 19 , 26 ], in which authors have obtained queue size distribution at various epochs. batch service queue with MV applies in many real-life queues, viz., telecommunication, transportation, manufacturing, etc.…”

An SMDP model for a multiclass multi-server queueing control problem considering conversion times

“…In literature, research on multi-server queueing problems is mainly categorized into two types. Some research focuses on analyzing the performance measures of the queueing systems in stationary state [7,9,18] contending for resources under a given policy, e.g. to analyze the performance measures such as the utilization of the servers, the workload balance of the servers, the queue length, the waiting time of the customers or the flow time of the customers under FCFS (First Come First Served) dispatching rule.…”