Scope and purpose

Discrete-time queueing theory is distinguished from its more developed continuous-time counterpart by the synchronous nature of its service. Time is divided into fixed-length slots and service of a customer typically takes an integer number of slots. Discrete-time queueing models are particularly appropriate to describe the various queueing related phenomena in digital computer and communication systems including mobile and B-ISDN networks based on asynchronous transfer mode (ATM) technology, due to the packetized nature of these transport protocols.

This work focuses on a discrete-time queueing system with server interruptions. Interruptions are an abstraction of temporary server unavailability. The latter can be caused by temporary occupancy of the server by other customers — regulated by a scheduling discipline such as round robin or priority scheduling — or temporary failure of the server (e.g. due to transmission errors, maintenance or repair). Typically, interruptions occurring in these systems have a bursty nature, i.e., they occur in bursts rather than being randomly spread over time. The presented model allows to study the effects of the burstiness of the server interruptions on various performance measures such as mean queue contents and mean customer delay. Two different operation strategies are hereby considered: after an interruption, service may either continue where it left off or it may completely restart.