Jñānābha‎, Vol. 50 (1) (2020), 144-157

N-POLICY FOR M/Ek/1 QUEUEING MODEL WITH SERVICE INTERRUPTION

By

Pankaj Sharma
Department of Mathematics, School of Science,
Noida International University, Gautam Budh Nagar, 203201, G. Noida, Uttar Pradesh, India
Email:sharma ibspankaj@rediffmail.com
(Received : May 29, 2019 ; Revised: May 18, 2020)


Abstract

This study deals with an unreliable single service station Erlangian queueing model with k-phase service and l-phase repair under N-policy. The arriving customers follow Poisson process with arrival rates dependent upon the state of the service station, which may be idle, operating, broken down, and under setup or repair states. Due to N-policy the service station turns on only when at least N(≥ 1) customers are accumulated in the system and turns off only when the system becomes empty. While providing service, the service station may breakdown according to Poisson process. An optimal operating N-policy is proposed to minimize the total expected cost. If the service station breakdowns, then it is sent for repair at the repair facility which renders repair after a set up time. After repairing, the service station works as good as before breakdown. Recursive technique and generating functions are employed for solution purpose. Explicit expressions for various performance indices are established. Cost analysis and sensitivity analysis have been done to explore the effects of different parameters.


2010 Mathematics Subject Classifications: 90B22, 60K25.
Keywords and phrases: N-Policy, Erlangian queue, Breakdown, Phase repair, Setup, Balking Recursive technique, Generating function, Cost analysis.