Abstract
This paper examines an MX/G/1 retrial model with negative customers including the concepts of working vacation, Bernoulli feedback, delayed repair, state-dependent and multi-optional services. Such a queue is quite relevant in real world, for instance in computer systems, manufacturing organisations, packet-switching networks, telecommunication systems, etc. The arrival pattern of customers is according to Poisson distribution. The service is such that first essential service (FES) is provided to every customer and second optional service (SOS) is provided in k phases to those who wants to opt for the same. The negative customers may arrive during the time when the server is busy in serving a positive customer. This leads to breakdown of the server and thus the server has to be restored (repair) by the repair man. Some moments may be taken by the repair man to initiate the repair process, leading to delay in repair. In our work, firstly we have calculated performance measures like long run probabilities and orbit size along with some reliability indices. Then a relative study between the exact expected waiting time and approximate expected waiting time of the system is presented via maximum entropy approach. Also we perform cost optimization using particle swarm optimization (PSO method). Few numerical results are also provided.
Highlights
This study deals with bulk arrival retrial G-queue where the server is subjected to state dependent and multi-optional services
In G-queues, a negative customer arrives only when server is occupied with a positive customer and forces it to leave the system thereby causing an interruption in the service
3.1 Queueing Measures In this subsection, we aim to find the long run probabilities of the state of the server as well as the queue size and waiting time of the customer which is a great source of information for making a model more sufficient and economically friendly
Summary
This study deals with bulk arrival retrial G-queue where the server is subjected to state dependent and multi-optional services. As per the literature survey, no work has been done on finding maximum entropy results and optimal parameters for an MX/G/1 retrial G-queue with multi-optional and state dependent service under Bernoulli feedback, working vacations as well as delayed repair. The hazard rates for retrial, busy (with FES and SOS), working vacation, repair and delayed repair state of the server respectively are as follows:. Let us denote the elapsed retrial time, elapsed service time (for FES and SOS), elapsed working vacation time, elapsed repair time (during FES and SOS) and elapsed delayed repair time (during FES and SOS) respectively by So(t), Bo(t), Bio(t), Bvo(t), Go(t), Gio(t), Ho(t) and Hio(t) These supplementary variables are introduced to achieve a bivariate Markov process {β(t), N(t); t≥0}, where β(t) is the state of the server {0, 1, 2, 3, 4, 5, 6} as described above.
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