On Markovian Queues With Single Working Vacation and Bernoulli Interruptions

Abstract

This paper considers the customers’ equilibrium and socially optimal joining–balking behavior in a single-server Markovian queue with a single working vacation and Bernoulli interruptions. The model is motivated by practical service systems where the service rate can be adjusted according to whether or not the system is empty. Specifically, we focus on a single-server queue in which the server's service rate is reduced from a regular to a lower one when the system becomes empty. This lower rate period is called a working vacation for the server which may represent that part of the service facility is under a maintenance process or works on other non-queueing job, or simply for saving the energy (for a machine server case). In this paper, we assume that the working vacation period is terminated after a random period or with probability p after serving a customer in a non-empty system. Such a system is called a queue with single working vacation and Bernoulli interruptions. Customers are strategic and can make choice of joining or balking based on different levels of system information. We consider four scenarios: fully observable, almost observable, almost unobservable, and fully unobservable queue cases. Under a reward-cost structure, we analyze the customer's equilibrium and social-optimal strategies. In addition, the effects of system parameters on optimal strategies are illustrated by numerical examples.

On Queues with Working Vacation and Interdependence in Arrival and Service Processes

“…The time away from the primary service center is called vacation and can be attributed to several factors. For a comprehensive and complete review of vacation queuing systems, we refer the readers to Doshi [9], Takagi [10], Tian and Zhang [11], Ke et al [12] and Chandrasekaran et al [13], who conducted a survey describing the latest research on the working vacation queueing system. Recently, Panta et al [14] surveyed vacation queuing models.…”

Strategic Analysis of Retrial Queues with Setup Times, Breakdown and Repairs

“…Tese queueing models are often used in computer systems and telecommunication networks. General models, methods, results, examples, and applications of retrial queues can be found in Artalejo and Gómez-Corral [1], Tian et al [2]. In recent years, Phung-Duc [3] used retrial queues to model cloud computing systems and gave the steady-state probabilities of the systems.…”