Analysis of a correlated queue in a communication system

A family of queues for which the service time B_n of customer n depends on the interarrival time I_n between customers n-1 and n and the random variables I_n and B_n exhibit a proportionality relation is studied. In particular, the focus is on dependencies that arise naturally in communication systems, where the finite speed of the communication links constrains the amount of data that can be received in a given time interval. The simple case of a deterministic proportionality relation between the service time of a customer and its preceding interarrival time is considered and extended to allow the addition of an independent, generally distributed overhead to the service time. Several models that capture the on-off behavior of communication links in packet networks are then addressed. In all cases, expressions for the delay experienced by a packet in the system and illustrative numerical examples are provided