In this paper the authors define an infinite server polling system. They propose to use the model to simulate the behaviour of vehicular traffic in a cross-road which is controlled by a semaphore system. This polling system model differs from the classical polling model. In fact, they assume that there are an infinite number of servers that move as a single group to serve the different queues in the system. So their study concerns the analysis of an M/G/∞-type polling model. The model contains N ≥ 2 infinite buffer queues attended by a group of ample number of servers that visit the queues in a cyclic fashion. The queues in the system are indexed by i = 1,2,...,N in the order of the servers’ movement. During the visit at queue i, the group of servers works at this queue for Vi units of time and it acts there as an M/G/∞ queue. The visit times are independent and identically distributed random variables. Customers arrive at all queues according to independent homogeneous Poisson processes with rate λi for queue i. After completing their service time, customers leave the system. The service time of each individual customer at queue i is denoted by Bi. It is assumed that all service times in one queue are independent and identically distributed random variables, which are mutually independent of all service times at any other queue. At the end of the visit to queue i, the group of servers moves to queue i+1, incurring a switch-over time Di, and a realization of Vi is drawn. It is assumed that {Di} is a sequence of independent random variables. Moreover, if the service of a customer of queue i is not completed during a single visit, then at the next visit, a new service time will be drawn from the service time distribution of Bi, for that particular customer. In this context the authors compute recursively the first moment and the probability generation function of the queue length distributions at a polling instant. They also derive the mean and the Laplace-Stieltjes transform of the sojourn time of a customer arriving at queue i, studying in particular the case where both the service time and the visit time at queue i are exponentially distributed. They also investigate how to optimize the visit order of servers at the various queues in the model so that the expected throughput of the system is maximized. Leonardo Pasini

Recensione dell'Articolo: (Vlasiou, M.; Yechiali, U. - " M/G/∞polling systems with random visit Times " - Probab.Engrg.Inform.Sci. 22 (2008), no.1, 81–105.)

PASINI, Leonardo
2009

Abstract

In this paper the authors define an infinite server polling system. They propose to use the model to simulate the behaviour of vehicular traffic in a cross-road which is controlled by a semaphore system. This polling system model differs from the classical polling model. In fact, they assume that there are an infinite number of servers that move as a single group to serve the different queues in the system. So their study concerns the analysis of an M/G/∞-type polling model. The model contains N ≥ 2 infinite buffer queues attended by a group of ample number of servers that visit the queues in a cyclic fashion. The queues in the system are indexed by i = 1,2,...,N in the order of the servers’ movement. During the visit at queue i, the group of servers works at this queue for Vi units of time and it acts there as an M/G/∞ queue. The visit times are independent and identically distributed random variables. Customers arrive at all queues according to independent homogeneous Poisson processes with rate λi for queue i. After completing their service time, customers leave the system. The service time of each individual customer at queue i is denoted by Bi. It is assumed that all service times in one queue are independent and identically distributed random variables, which are mutually independent of all service times at any other queue. At the end of the visit to queue i, the group of servers moves to queue i+1, incurring a switch-over time Di, and a realization of Vi is drawn. It is assumed that {Di} is a sequence of independent random variables. Moreover, if the service of a customer of queue i is not completed during a single visit, then at the next visit, a new service time will be drawn from the service time distribution of Bi, for that particular customer. In this context the authors compute recursively the first moment and the probability generation function of the queue length distributions at a polling instant. They also derive the mean and the Laplace-Stieltjes transform of the sojourn time of a customer arriving at queue i, studying in particular the case where both the service time and the visit time at queue i are exponentially distributed. They also investigate how to optimize the visit order of servers at the various queues in the model so that the expected throughput of the system is maximized. Leonardo Pasini
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11581/333781
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