A queue with server of walking type (autonomous service)

Queues with autonomous service (QAS) represent service systems in which the server becomes unavailable for a random time after each service epoch. Such systems have been used to model secondary memory devices in computer systems (e.g. paging disks or drums). The queue with server of walking type studied by Skinner [1] is a special instance of our model. This model has also been considered by Borovkov [2]. Assuming general independent interarrival times we obtain an operational formula relating the waiting time in stationary state of a QAS to the waiting time of a GI/G/l queue. This result dispenses the need for analysis of the QAS in special cases and generalizes the result of Skinner [1], or that of Coffman [3] for a paging drum. Sufficient conditions for stability or instability of the system are also obtained.