Collection of customers

Abstract

This paper analyses a variant of the ikl/G/l queue in which the service times of arriving customers depend on the length of the interval between their arrival and the previous arrival.The dependence structure corresponds to the case of customers arriving according to an ordinary Poisson arrival process, and customer collectors being sent out according to a Poisson process to collect the customers and to bring them to the service facility.In this case collected numbers of customers, and hence total collected service requests, are positively correlated with the corresponding collect intervals.Viewing a batch of collected customers as one (super) customer gives rise to an itf/G/l queue with a positive correlation between service times of such customers and their interarrival times.Both for individual customers and for batches of collected customers we derive the transforms of the sojourn time and waiting time distributions.We also compare our results with those for the ordinary M/G/l queue without dependence.

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