Optimal Pricing Analysis of Computer Networks Based on a Queueing System With Retrial Mechanism

Abstract

We consider a single-server retrial queue with a Poisson arrival process and exponential service times, where the server is unreliable. Assume there is no waiting space in front of the server and the customer who finds the server unavailable joins an orbit to access the server some time later. We discuss two types of customers' retrial behavior. One is that each customer in the orbit seeks for services independently and the total retrial rate of the system depends on the number of customers in the orbit. The other type of retrial discipline is called constant retrial policy and it arises from some situations in the computer and communication network where the retrial rate may be controlled by automatic mechanisms. An announced price charged by the server is imposed on customers joining the system and the actual demands for services depend on the price via a decreasing function. We investigate the system characteristics and study how the manager, whose goal is to maximize its own profit, determines the price charging joining customers. Finally, we present an application example to illustrate the obtained results and make comparisons between the two retrial policies from the perspective of customers' expected waiting time.

Analysis of a Retrial Queue With Two-Type Breakdowns and Delayed Repairs

“…Most unreliable retrial queues assume that the server can be immediately repaired when it breaks down. For example, Zhang [32] studied an M/M/1 retrial queue with passive breakdowns and active breakdowns from economic point, in which whenever any type of breakdowns occurs, the sever immediately enters a repair stage and the repair times for these two types of breakdowns are identical and exponential distribution. Zirem et al [33]dealt with a batch arrivals retrial queue with active breakdowns, where the sever can be immediately repaired when breakdown happens and reserved service schedule is considered for the interrupted customer.…”

Optimal Production Control of Remanufacturing Systems Based on a Queueing Model With Returns

“…As we know, stochastic fluid model is useful in simulating various kinds of high speed systems [8]. Queueing models are very popular and useful to analyze the stochastic service systems [9], [10], [11]. In this paper, we take the queueing theory and Markov decision process to analyze the optimal control of a remanufacturing system.…”