In this paper the authors study the M/G/infty tollbooth tandem model with an infinite number of homogeneous servers. This delay system is characterized by the fact that customers must depart in the order they arrive. Customer service time has an arbitrary distribution. The authors are concerned with the probability distribution of the following quantities of interest, which are functions of t : the number of customers in the system at time $t$ , the number of departure-delayed customers in the system at time $t$ , the number of departures by time $t$ , the time spent in the system by a customer who arrived at time t , the departure delay of a customer who arrived at time $t$ and the number of customers left behind by a departing customer who arrived at time t . The authors first consider the case when the customer arrival process is Poisson, and they obtain the closed form solution for the random processes described above, as well as the corresponding steady state distributions. The authors extend the results to the case of batch Poisson and nonhomogeneous Poisson arrival processes.
Recensione dell'articolo:(Chao, Xiuli; He, Qi-Ming; Ross, Sheldon - "Tollbooth tandem queues with infinite homogeneous servers." - J. Appl. Probab. 52 (2015), no. 4, 941-961.) MR3439164 MathSciNet ISSN 2167-5163
Leonardo Pasini
2016-01-01
Abstract
In this paper the authors study the M/G/infty tollbooth tandem model with an infinite number of homogeneous servers. This delay system is characterized by the fact that customers must depart in the order they arrive. Customer service time has an arbitrary distribution. The authors are concerned with the probability distribution of the following quantities of interest, which are functions of t : the number of customers in the system at time $t$ , the number of departure-delayed customers in the system at time $t$ , the number of departures by time $t$ , the time spent in the system by a customer who arrived at time t , the departure delay of a customer who arrived at time $t$ and the number of customers left behind by a departing customer who arrived at time t . The authors first consider the case when the customer arrival process is Poisson, and they obtain the closed form solution for the random processes described above, as well as the corresponding steady state distributions. The authors extend the results to the case of batch Poisson and nonhomogeneous Poisson arrival processes.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
