Bonfring International Journal of Research in Communication Engineering
Online ISSN: 2277-5080 | Print ISSN: 2250-110X | Frequency: 4 Issues/Year
Impact Factor: 0.528 | International Scientific Indexing(ISI) calculate based on International Citation Report(ICR)
Analysis of a Poisson Bulk Arrival Single Service Queueing Model with Threshold Policy on Number of Primary Services for Secondary Jobs
Abstract:
In this paper the concentration is on the analysis of an eqn Queueing system with threshold policy on number of primary services for secondary jobs. In most of the queueing systems with vacations, the operator of the service station will be allotted to secondary jobs (vacations) only if, the system becomes empty. But it may not be the case always; there are situations in which the operator has to shutdown the machine after some finite number of processes. Addressing this, it is assumed that after, rendering M consecutive services, the operator of the service station closes the service and avails a vacation of random length. At a vacation completion epoch, if the number of waiting customers in the queue is less than a threshold value N (N > M), then the operator waits in the system (dormant period) till it reaches N. At a vacation completion epoch or during a dormant period, if the queue length is at least N, then the server starts the service. For the proposed queueing model, the probability generating function of the expected number of customers in the system at an arbitrary time is derived. Expected length of the system, busy period and idle period are derived. An optimum policy for total average cost is also discussed. Numerical illustrations are provided.
Keywords: Bulk Queue, Multiple Vacations, Dormant Period, Steady State Solution.
Volume: 2 | Issue: 4
Pages: 21-27
Issue Date: December , 2012
DOI: 10.9756/BIJRCE.8397
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