Analysis of a correlated queue in a communication system

A family of queues is studied for which the service time B_n of customer n and the interarrival time I_n between customers n-1 and n exhibit some sort of proportionality. The focus is on dependencies that arise naturally in the context of 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. This is extended to allow the addition of an independent, generally distributed overhead to the service time of each customer. Several models that capture the ON-OFF behavior of communication links in packet networks are considered. In all cases, expressions for the delay experienced by a packet in the system are provided. Numerical examples illustrate the impact of dependencies through comparison with less accurate models. The results should be of relevance to environments other than communication as well