A survey of the machine interference problem

This paper surveys the research published on the machine interference problem since the 1985 review by Stecke & Aronson. After introducing the basic model, we discuss the literature along several dimensions. We then note how research has evolved since the 1985 review, including a trend towards the modelling of stochastic (rather than deterministic) systems and the corresponding use of more advanced queuing methods for analysis. We conclude with some suggestions for areas holding particular promise for future studies.Natural Sciences and Engineering Research Council (NSERC) Discovery Grant 238294-200

Equilibrium Customer Strategies in the Single-Server Constant Retrial Queue with Breakdowns and Repairs

We consider a single-server constant retrial queueing system with a Poisson arrival process and exponential service and retrial times, in which the server may break down when it is working. The lifetime of the server is assumed to be exponentially distributed and once the server breaks down, it will be sent for repair immediately and the repair time is also exponentially distributed. There is no waiting space in front of the server and arriving customers decide whether to enter the retrial orbit or to balk depending on the available information they get upon arrival. In the paper, Nash equilibrium analysis for customers’ joining strategies as well as the related social and profit maximization problems is investigated. We consider separately the partially observable case where an arriving customer knows the state of the server but does not observe the exact number of customers waiting for service and the fully observable case where customer gets informed not only about the state of the server but also about the exact number of customers in the orbit. Some numerical examples are presented to illustrate the effect of the information levels and several parameters on the customers’ equilibrium and optimal strategies

Performance Analysis of a Retrial Queueing System with Optional Service, Unreliable Server, Balking and Feedback

This paper considers a Markovian retrial queueing system with an optional service, unreliable server, balking and feedback. An arriving customer can avail of immediate service if the server is free. If the potential customer encounters a busy server, it may either join the orbit or balk the system. The customers may retry their request for service from the orbit after a random amount of time. Each customer gets the First Essential Service (FES). After the completion of FES, the customers may seek the Second Optional Service (SOS) or leave the system. In the event of unforeseen circumstances, the server may encounter a breakdown, at which point an immediate repair process will be initiated. After the service completion, the customer may leave the system or re-join the orbit if not satisfied and demand regular service as feedback. In this investigation, the stationary queue size distributions are framed using a recursive approach. Various system performance measures are derived. The effects induced by the system parameters on the performance metrics are numerically and graphically analysed

Optimal Pricing Effect on Equilibrium Behaviors of Delay-Sensitive Users in Cognitive Radio Networks

This paper studies price-based spectrum access control in cognitive radio networks, which characterizes network operators' service provisions to delay-sensitive secondary users (SUs) via pricing strategies. Based on the two paradigms of shared-use and exclusive-use dynamic spectrum access (DSA), we examine three network scenarios corresponding to three types of secondary markets. In the first monopoly market with one operator using opportunistic shared-use DSA, we study the operator's pricing effect on the equilibrium behaviors of self-optimizing SUs in a queueing system. %This queue represents the congestion of the multiple SUs sharing the operator's single \ON-\OFF channel that models the primary users (PUs) traffic. We provide a queueing delay analysis with the general distributions of the SU service time and PU traffic using the renewal theory. In terms of SUs, we show that there exists a unique Nash equilibrium in a non-cooperative game where SUs are players employing individual optimal strategies. We also provide a sufficient condition and iterative algorithms for equilibrium convergence. In terms of operators, two pricing mechanisms are proposed with different goals: revenue maximization and social welfare maximization. In the second monopoly market, an operator exploiting exclusive-use DSA has many channels that will be allocated separately to each entering SU. We also analyze the pricing effect on the equilibrium behaviors of the SUs and the revenue-optimal and socially-optimal pricing strategies of the operator in this market. In the third duopoly market, we study a price competition between two operators employing shared-use and exclusive-use DSA, respectively, as a two-stage Stackelberg game. Using a backward induction method, we show that there exists a unique equilibrium for this game and investigate the equilibrium convergence.Comment: 30 pages, one column, double spac

Sharing delay information in service systems: a literature survey

Service providers routinely share information about upcoming waiting times with their customers, through delay announcements. The need to effectively manage the provision of these announcements has led to a substantial growth in the body of literature which is devoted to that topic. In this survey paper, we systematically review the relevant literature, summarize some of its key ideas and findings, describe the main challenges that the different approaches to the problem entail, and formulate research directions that would be interesting to consider in future work

An optional service Markovian queue with working disasters and customer’s impatience

In this paper, we develop a new class of Markov model with working disasters, second optional service, and reneging of customers. The disasters can occur during regular busy period. Whenever a disaster occurs, server continues to serve the customers with a lower service rate instead of completely stopping the service and after the completion of disaster recovery it switches to the regular busy period. Steady-state solution of the model is obtained by using probability generating function technique and stability condition is derived. Further, some important performance measures are presented. A cost model is developed in order to obtain the optimal service rates during first essential service, second optional service and during disaster period using quadratic fit search method. At the end, we provide some numerical examples to visualize the applicability of the model in practical situations.Publisher's Versio

Strategic queueing behavior for individual and social optimization in managing discrete time working vacation queue with Bernoulli interruption schedule

In this paper, we consider a discrete time working vacation queue with a utility function for the reward of receiving the service and the cost of waiting in the system. A more flexible switching mechanism between low and regular service states is introduced to enhance the practical value of the working vacation queue. Under different precision levels of the system information, namely observable, almost unobservable and fully unobservable cases, the utility function is studied from both the individual customer’s and the system administrator’s points of view. By analyzing the steady-state behavior of the system, the associated optimal joining decisions under different information scenarios are obtained. We find that for the fully observable queue, the joining threshold for individual optimization may be less than the one for social optimization in working vacation period. A similar situation also appears in almost unobservable case. Such phenomenon is not possible for the classic first come first served queue due to the fact that there is no vacation time and thus will not cause large fluctuations in customers’ conditional waiting time. Additionally, we also conduct some numerical comparisons to demonstrate the effect of the information levels as well as system parameters on customer joining behavior.This research was partially supported by grant from NSERC DAS programs, National Natural Science Foundation of China (Nos.71301111, 71571127, 71402072) and the FSUSE (No.2012RC23).http://www.elsevier.com/locate/caor2017-09-30hb2016Electrical, Electronic and Computer Engineerin