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An M/M/1 constant retrial queue with balking customers and set-up time is considered. Once the system becomes empty, the server will be turned down to reduce operating costs, and it will be activated only when there is a customers arrives. In this paper, the almost unobservable case is studied, in which the information of the queue length is unavailable, whereas the state of the server can be obtained. Firstly, the steady state solutions are derived and the individual equilibrium strategies are analyzed. In addition, social optimization problems, including cost analysis and social welfare maximization are investigated by using the PSO algorithm. Finally, by appropriate numerical examples, the sensitivity of some main system parameters is shown.

This study examines a matching queue problem (double-sided matching queue) where customers are loss-averse with respect to their waiting times. We first set the reference point and construct the lo...

In some queueing systems, customers are frequently asked for giving a service quality feedback for their service at their service completion instants. Based on this phenomenon, in this paper, we model this type of queueing systems as clearing queues with service quality feedback and system maintenance. Once the system receives an unsatisfied (negative) feedback from customers (i.e., a customer is unsatisfied with the service), the system undergoes an adjustment procedure, and at the same time, all the present customers are forced to leave the system. By considering the waiting cost and reward, we discuss the joining behavior of customers and, respectively, derive the corresponding equilibrium joining strategies and social optimal strategies under different levels of information (the observable and the unobservable cases). Finally, some numerical examples are provided to show the effect of several system parameters on the equilibrium and optimal balking strategies.

This paper investigates an M/M/1 constant retrial queue with reserved time and vacations. A new arriving customer will take up the server and accept service immediately if the server is idle. Otherwise, if the server is busy or on vacation, customers have to join a retrial orbit and wait for retry. Once a service is completed, the server will reserve a random time to seek a customer from the orbit at a constant retrial rate. If there is no arrivals (from the orbit or outside) during the idle period, to save energy, the server will take a vacation. This paper studies the fully unobservable case. First, the steady-state condition of the system is analyzed by using the Foster’s criterion, and the customers’ expected waiting time is obtained based on the generating function technique. And then, by introducing an appropriate revenue structure, the equilibrium strategies of customers and the socially optimal strategy are all derived. Furthermore, a comparison between them is made and the effect of some main system parameters is studied.

The existing tollbooth systems with multi-type vehicles in transportation literature typically assume the servers are either dedicated for each vehicle type or generic for all vehicle types. Conversely, in this paper, we focus on studying two similar systems both with skill-based servers, i.e., each tollbooth can handle a given subset of vehicle types. Meanwhile, we assume that vehicles queue together in a single lane, thus they get served by global First-Come-First-Served discipline. The slight difference between these two systems is the number of exits: one with a single exit (model 1) and the other with two exits (model 2). Nevertheless, it creates large difference in the resolving process. By spectral expansion technique, we obtain a closed-form solution for the system’s steady-state probabilities in the former model and the explicit solution without closed-form expressions in the latter model. By numerical results, we demonstrate how the parameters selection influences system’s performance, along with some intriguing managerial insights. We also use the system of the same structure but with dedicated servers as the baseline for comparisons to show the benefits of skill-based servers.

In this paper we consider a batch matching system with impatient servers and boundedly rational customers, which is essentially a double-ended batch service system. Each server is responsible for a batch of customers and serves them instantaneously. Especially, we assume that the servers have the characteristic of ”impatience”, which will lead to incomplete batch processing of each service. To derive the stationary distribution of system states, we combine two methods (called probability generating function method and G-matrix method), and some main performance measures are captured. In addition, we assume the customers are boundedly rational, that is, they are unable to estimate their sojourn times and utilities accurately. To deal, a logit model is employed to model this characteristic of the customers, and by which, we obtain the customers’ equilibrium joining fraction which is compared with the equilibrium joining probability of fully rational customers afterwards. Depending on whether the service is visible or invisible, we conduct some numerical analyses to show main parameters’ impact on equilibrium fraction, along with some intuitive explanations. Finally, to make the system viable economically, a function of service provider’s utility is developed and several numerical plots are presented to study the impact of several main parameters on the utility. Through the PSO (Particle Swarm Optimization) algorithm, we numerically obtain the maximum utility point within a certain range of multiple parameters.