Antonis Economou

Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs

We consider the Markovian single-server queue that alternates between on and off periods. Upon arriving, the customers observe the queue length and decide whether to join or balk. We derive equilibrium threshold balking strategies in two cases, according to the information for the servers state.

Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes

We consider a Markovian queue subject to Poisson generated catastrophes. When- ever a catastrophe occurs, all customers are forced to abandon the system, the server is rendered inoperative and an exponential repair time is set on. We assume that the arriving customers decide whether to join the system or balk, based on a natural reward-cost structure. We study the balking behavior of the customers and derive the corresponding Nash equilibrium strategies.

Analysis of a Multiserver Queue with Setup Times

This paper deals with the analysis of an M/M/c queueing system with setup times. This queueing model captures the major characteristics of phenomena occurring in production when the system consists in a set of machines monitored by a single operator. We carry out an extensive analysis of the system including limiting distribution of the system state, waiting time analysis, busy period and maximum queue length.

Optimal balking strategies in single-server queues with general service and vacation times

Abstract In many service systems arising in OR/MS applications, the servers may be temporarily unavailable, a fact that affects the sojourn time of a customer and his willingness to join. Several studies that explore the balking behavior of customers in Markovian models with vacations have recently appeared in the literature. In the present paper, we study the balking behavior of customers in the single-server queue with generally distributed service and vacation times. Arriving customers decide whether to enter the system or balk, based on a linear reward–cost structure that incorporates their desire for service, as well as their unwillingness to wait. We identify equilibrium strategies and socially optimal strategies under two distinct information assumptions. Specifically, in a first case, the customers make individual decisions without knowing the system state. In a second case, they are informed about the server’s current status. We examine the influence of the information level on the customers’ strategic response and we compare the resulting equilibrium and socially optimal strategies.

A continuous-time Markov chain under the influence of a regulating point process and applications in stochastic models with catastrophes

Abstract We consider a continuous-time Markov chain { N (t), t⩾0} with state space S. A point process {X(t), t⩾0} , using a function A:[0,∞)→S in the following way, influences the evolution of { N (t)} : whenever an event of {X(t)} occurs at time t, the Markov chain of interest goes immediately at state A(t) and evolves according to the dynamics of { N (t)} until the next event of {X(t)} and so on. We study the transient and the limiting distribution of the resulting process and prove some stochastic comparison facts. Several examples that demonstrate the applicability of the model are also included.

Applications of maximum queue lengths to call center management

This paper deals with the distribution of the maximum queue length in two-dimensional Markov models. In this framework, two typical assumptions are: (1) the stationary regime, and (2) the system homogeneity (i.e., homogeneity of the underlying infinitesimal generator). In the absence of these assumptions, the computation of the stationary queue length distribution becomes extremely intricate or, even, intractable. The use of maximum queue lengths provides an alternative queueing measure overcoming these problems. We apply our results to some problems arising from call center management.

Product form stationary distributions for queueing networks with blocking and rerouting

In this paper we study Markovian queueing networks in which the service and the routing characteristics have a particular form which leads to a product form stationary distribution for the number of customers in the various queues of the network. We show that if certain transitions are prohibited due to blocking conditions, then the form of the stationary distribution is preserved under a certain rerouting protocol. Several examples are presented which illustrate the wide applicability of the model.

Equilibrium balking strategies for a clearing queueing system in alternating environment

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.

On the number of recovered individuals in the SIS and SIR stochastic epidemic models.

The basic models of infectious disease dynamics (the SIS and SIR models) are considered. Particular attention is paid to the number of infected individuals that recovered and its relationship with the final epidemic size. We investigate this descriptor both until the extinction of the epidemic and in transient regime. Simple and efficient methods to obtain the distribution of the number of recovered individuals and its moments are proposed and discussed with respect to the previous work. The methodology could also be extended to other stochastic epidemic models. The theory is illustrated by numerical experiments, which demonstrate that the proposed computational methods can be applied efficiently. In particular, we use the distribution of the number of individuals removed in the SIR model in conjunction with data of outbreaks of ESBL observed in the intensive care unit of a Spanish hospital.

Algorithmic analysis of the Geo/Geo/c retrial queue

In this paper, we consider a discrete-time queue of Geo/Geo/c type with geometric repeated attempts. It is known that its continuous counterpart, namely the M/M/c queue with exponential retrials, is analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused from the retrial feature. In discrete-time, the occurrence of multiple events at each slot increases the complexity of the model and raises further computational difficulties. We propose several algorithmic procedures for the efficient computation of the main performance measures of this system. More specifically, we investigate the stationary distribution of the system state, the busy period and the waiting time. Several numerical examples illustrate the analysis.