Jinbiao Wu

An M/G/1 retrial G-queue with preemptive resume and feedback under N-policy subject to the server breakdowns and repairs

An M/G/1 retrial G-queue with preemptive resume and feedback under N-policy vacation subject to the server breakdowns and repairs, is investigated in this paper. Arrivals of both positive customers and negative customers are two independent Poisson processes, and positive customers receive service immediately if the server is free upon their arrivals. Otherwise, they may enter a retrial orbit and try their luck after a random time interval. All positive customers must receive preliminary first phase of service and primary second phase of service. While at the preliminary service, the server may push out the customer undergoing such service to the orbit, to commence preliminary service of an arriving positive customer. Negative customers not only remove the customer being in service, but also make the server under repair. The server leaves for an N-policy vacation as soon as the system empties. By applying the supplementary variables method, we obtain the steady-state solutions for both queueing measures and reliability quantities. The effects of various parameters on the system performance are analyzed numerically.

An M/G/1 retrial G-queue with non-exhaustive random vacations and an unreliable server

This paper deals with an M/G/1 retrial queue with negative customers and non-exhaustive random vacations subject to the server breakdowns and repairs. Arrivals of both positive customers and negative customers are two independent Poisson processes. A breakdown at the busy server is represented by the arrival of a negative customer which causes the customer being in service to be lost. The server takes a vacation of random length after an exponential time when the server is up. We develop a new method to discuss the stable condition by finding absorb distribution and using the stable condition of a classical M/G/1 queue. By applying the supplementary variable method, we obtain the steady-state solutions for both queueing measures and reliability quantities. Moreover, we investigate the stochastic decomposition law. We also analyse the busy period of the system. Some special cases of interest are discussed and some known results have been derived. Finally, an application to cellular mobile networks is provided and the effects of various parameters on the system performance are analysed numerically.

Equilibrium strategies of the unobservable M/M/1 queue with balking and delayed repairs

The balking strategies for a queue with breakdowns and delayed repairs is studied.We provide supplement to Wang and Zhang (2011) by studying the unobservable cases.The model is viewed as an M/M/1 queue that operates in a random environment.From a methodological point of view, the almost unobservable case is interesting. Wang and Zhang (2011) studied the equilibrium threshold balking strategies for the fully observable and partially observable single-server queues with server breakdowns and delayed repairs. Customers decide whether to join or balk the system based on observation of the queue length and status of the server at their arrival instants. The present paper aims to study the corresponding unobservable cases in which the queue length is unknown to arriving customers. The model under consideration can be viewed as an M/M/1 queue in a random environment. Equilibrium mixed strategies are derived for the almost unobservable and fully unobservable queues. Finally, we illustrate the effect of several system parameters on the equilibrium behavior via numerical examples.

Heavy-traffic asymptotics of a priority polling system with threshold service policy

In this paper, by the singular-perturbation technique, we investigate the heavy-traffic behavior of a priority polling system with three queues under threshold policy. It turns out that the scaled queue-length of the critically loaded queue is exponentially distributed, independent of that of the stable queues, which possess the same distributions as a two-class priority queue with N-policy vacation. Further, we provide an approximation of the tail queue-length distribution of the stable queues, which shows that it has the same prefactors and decay rates as the classical two-class preemptive priority queue. Stochastic simulations are taken to support the results. HighlightsThe heavy-traffic behavior of a polling system with threshold policy is discussed.The scaled queue-length of the critically loaded queue is exponentially distributed.Approximations of queue lengths of the stable queues are provided.The decay rates of the stable queues are the same decay rate as the classical preemptive priority queues.

Maximum principle for mean-field zero-sum stochastic differential game with partial information and its application to finance

Abstract In this paper, we investigate the stochastic optimal control problem for the zero-sum stochastic differential game of mean-field type with partial information. We derive a necessary and sufficient maximum principle for that problem by virtue of the duality method and the mean-field backward stochastic differential equations. As an application, we apply the result to the mean-field stochastic differential portfolio game problem, and obtain an equilibrium point of such game.

A re-examination of experience service offering and regular service pricing under profit maximization

A firm may offer an experience service free of charge to attract more customers to buy its regular service. This paper provides an economic analysis for interactions between the capacity-constrained firm and its waiting-averse customers, generating certain managerial insights. Free services should be sped up to move customers onto the paid service if it is idle, or slowed down to hold onto customers and avoid exacerbating congestion in the paid service if it is busy. A lower price should be charged for the regular service as compensation to customers for service delay if more of them buy that service. When more customers arrive for experience services, a greater price reduction should be offered to attract them into the regular service if it becomes more congested.

Optimal control of mean-field backward doubly stochastic systems driven by Itô-Lévy processes

ABSTRACT In this paper, we introduce a new class of backward doubly stochastic differential equations (in short BDSDE) called mean-field backward doubly stochastic differential equations (in short MFBDSDE) driven by Itô-Lévy processes and study the partial information optimal control problems for backward doubly stochastic systems driven by Itô-Lévy processes of mean-field type, in which the coefficients depend on not only the solution processes but also their expected values. First, using the method of contraction mapping, we prove the existence and uniqueness of the solutions to this kind of MFBDSDE. Then, by the method of convex variation and duality technique, we establish a sufficient and necessary stochastic maximum principle for the stochastic system. Finally, we illustrate our theoretical results by an application to a stochastic linear quadratic optimal control problem of a mean-field backward doubly stochastic system driven by Itô-Lévy processes.