Retrial queue

About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.

Analysis of a Constant Retrial Queue with Joining Strategy and Impatient Retrial Customers

Abstract: This paper treats an M/M/1 retrial queue with constant retrial times. If the server is busy at the arrival epoch, the arriving customer decides to join the retrial orbit with probability or balk with probability . Only the customer at the head of the orbit is permitted to access the server. Upon retrial, the customer immediately receives his service if the server is idle; otherwise, he may enter the orbit again or leave the system because of impatience. First, we give the performance analysis for this retrial queue and give some important performance indices. Second, based on a natural reward-cost structure, we analyze the Nash equilibrium customers’ joining strategies and give some numerical examples.

Optimal control of M/M/1 queueing system with constant retrial rate and non-reliable removable server

Abstract: The paper is concerned with the optimal control with respect to N-policy of the M/M/1 queue with constant retrial rate and non-reliable removable server. According to the N-policy, the server can start service only when the number of customers in the system reaches level N (N ≥ 1). We perform a steady-state analysis of the corresponding continuous-time Markov chain and calculate optimal threshold level to minimize the longrun average losses given cost structure.

Tail Asymptotics for a Retrial Queue with Bernoulli Schedule

Abstract: In this paper, we study the asymptotic behavior of the tail probability of the number of customers in the steady-state $M/G/1$ retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail. Detailed tail asymptotic properties are obtained for the (conditional and unconditional) probability of the number of customers in the (priority) queue, orbit and system, respectively.

Strategic Joining and Pricing Policies in a Retrial Queue With Orbital Search and Its Application to Call Centers

Abstract: This paper treats strategic joining and pricing policies in an M/M/1 retrial queue with orbital search which is motivated by the application in call centers, where the server will make orbital search or remain idle whenever he completes a service, the orbital search time follows exponential distribution. Given a natural reward-cost structure and imposed on an admission fee, all arriving customers decide to whether to join the orbit or balk when they find the server busy. Using queueing theory and game theory, we first analyze the Nash equilibrium mixed joining strategy for individual customer. Further we investigate the optimal joining probabilities and corresponding admission pricing problems that maximize the administrator's revenue and social profit, respectively. Finally, we present some numerical examples to demonstrate the effect of some system parameters on the sensitivity of the solutions of the individual maximization, administrator's maximization and social optimization.

Performance Analysis of an Unreliable $M/G/1$ Retrial Queue with Two-way Communication

Abstract: Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an $M/G/1$ retrial queue is investigated where the single server, subject to active failures, primarily attends incoming calls and directs outgoing calls only when idle. The incoming calls arriving at the server follow a Poisson arrival process, while outgoing calls are made in an exponentially distributed time. On finding the server unavailable (either busy or temporarily broken down), incoming calls intrinsically join the virtual orbit from which they re-attempt for service at exponentially distributed time intervals. The system stability condition along with probability generating functions for the joint queue length distribution of the number of calls in the orbit and the state of the server are derived and evaluated numerically in the context of mean system size, server availability, failure frequency and orbit waiting time.