Sensitivity analysis of a single server finite-source retrial queueing system with two-way communication and catastrophic breakdown using simulation

Abstract

In this paper, a finite-source retrial queueing system with twoway communication is investigated with the help of a simulation program of own. If a randomly arriving request from the finite-source finds the single server idle its service starts immediately, otherwise it joins an orbit from where it generates retrial/repeated calls after a random time. To increase the utilization of the server when it becomes idle after a random time an outgoing request is called for service from an infinity source. Upon its arrival if the server is busy, it goes to a buffer and when the server becomes idle again its service starts immediately. requests arriving from the finite-source and orbit are referred to as primary or incoming ones while requests called from the infinite source are referred to as secondary or outgoing requests, respectively. The service times of the primary and secondary requests are supposed to be random variables having different distributions. However, randomly catastrophic failures may happen to all the requests in the system, that is from the orbit, the service unit, and the buffer. In this case, the primary requests return to the finite-source, and the secondary ones are lost. The operation of the system is restored after a random time. Until the restoration is finished no arrivals and service take place in the system. All the above-mentioned times are supposed to be independent random variables. The novelty of this paper is to perform a sensitivity analysis of the failure and restoration/repair times on the main characteristics to illustrate the effect of different distributions having the same average and variance value. Our aim is to determine the distribution of the number of requests in the system, the average response time of an arbitrary primary request without successful service, also the average response time of an arbitrary and successfully served primary request, the total utilization of the service unit, or the probability that a primary request leaves the system without successful service because of a catastrophic event. Results are illustrated graphically obtained by our simulation program.