• MAXIMUM ENTROPY ANALYSIS OF UNRELIABLE SERVER MX/G/1 QUEUE WITH ESSENTIAL AND MULTIPLE OPTIONAL SERVICES

Rachna Vashishtha Pandey*, Piyush Tripathi

Abstract


In this paper we use the maximum entropy principle(MEP) to find the approximate waiting time of an MX/G/1 model with ‘k’ services; the first being essential (first essential service FES) whereas remaining ‘k-1’ of them as optional services (multiple optional service MOS). The server is subject to breakdown while rendering service to the customers. The customers arrive in the system in Poisson fashion in batches with arrival rate. After getting FES, the customer may opt for first of MOS, with some probability; after completing it, he may opt for next MOS with some other probability and so on. The service time of FES is generally distributed, while service times of MOS are exponentially distributed. The noble feature of the present study is to employ MEP which helps us in finding precise performance measures. The derived approximate results based on MEP, are compared with exact results obtained in previous studies for different distributions as special cases. It is noticed that MEP provides an alternative approach for solving complex queueing systems, in particular when queue size distribution is to be computed.


Keywords


Unreliable server, Bulk queue, Essential service, Multiple Optional services, Maximum entropy, Waiting time.

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