We consider a state-dependent single-server queue with orbit. This is a versatile model for the study of service systems, where the server needs a non-negligible time to retrieve waiting customers every time he completes a service. This situation arises typically when the customers are not physically present at a system, but they have a remote access to it, as in a call center station, a communication node, etc. We introduce a probabilistic approach for the performance evaluation of this queueing system, that we refer to as the queueing and Markov chain decomposition approach. Moreover, we discuss the applicability of this approach for the performance evaluation of other non-Markovian service systems with state dependencies.
We consider a transportation station, where customers arrive according to a Poisson process, observe the delay information and the fee imposed by the administrator and decide whether to use the facility or not. A transportation facility visits the station according to a renewal process and serves all present customers at each visit. We assume that every customer maximizes her individual expected utility and the administrator is a profit maximizer. We model this situation as a two‐stage game among the customers and the administrator, where customer strategies depend on the level of delay information provided by the administrator. We consider three cases distinguished by the level of delay information: observable (the exact waiting time is announced), unobservable (no information is provided) and partially observable (the number of waiting customers is announced). In each case, we explore how the customer reward for service, the unit waiting cost, and the intervisit time distribution parameters affect the customer behavior and the fee imposed by the administrator. We then compare the three cases and show that the customers almost always prefer to know their exact waiting times whereas the administrator prefers to provide either no information or the exact waiting time depending on system parameters.
We consider a fluid queue with two modes of service, that represents a production facility, where the processing of the customers (units) is typically carried out at a much faster time-scale than the machine-related processes. We examine the strategic behavior of the customers, regarding the joining/balking dilemma, under two levels of information upon arrival. Specifically, just after arriving and before making the decision, a customer observes the level of the fluid, but may or may not get informed about the state of the server (fast/slow). Assuming that the customers evaluate their utilities based on a natural reward/cost structure, which incorporates their desire for processing and their unwillingness to wait, we derive symmetric equilibrium strategy profiles. Moreover, we illustrate various effects of the information level on the strategic behavior of the customers. The corresponding social optimization problem is also studied and the inefficiency of the equilibrium strategies is quantified via the Price of Anarchy (PoA) measure.
The performance analysis of the classical M / G / 1 queue, under a general mixed joining/balking strategy was carried out recently by Kerner (Stoch Mod 24:364–375, 2008), who used an analytic approach based on the supplementary variable method. The tractability of the corresponding queueing system with state-dependent arrival rates is particularly significant, as it has important applications in situations where the customers are strategic. In this paper, we present an alternative path for the analysis of the same system, using purely probabilistic arguments.
We consider a transportation station, where customers arrive according to a Poisson process. A transportation facility visits the station according to a renewal process and serves at each visit a random number of customers according to its capacity. We assume that the arriving customers decide whether to join the station or balk, based on a natural reward-cost structure. We study the strategic behavior of the customers and determine their symmetric Nash equilibrium strategies under two levels of information.
We consider a Markovian clearing queueing system, where the customers are accumulated according to a Poisson arrival process and the server removes all present customers at the completion epochs of exponential service cycles. This system may represent the visits of a transportation facility with unlimited capacity at a certain station. The system evolves in an alternating environment that influences the arrival and the service rates. We assume that the arriving customers decide whether to join the system or balk, based on a natural linear reward-cost structure. We study the balking behavior of the customers and derive the corresponding Nash equilibrium strategies under various levels of information.
National and Kapodistrian University of Athens Department of Mathematics Zografou Athens, 15784 Greece email@example.com (0030) 210 7276405