Analysis of a discrete-time GI–G–1 queueing model subjected to bursty interruptions

Abstract

In this contribution, we investigate a discrete-time single-server queue subjected to server interruptions generated by a 2-state Markov process. The model under consideration assumes customers with multiple-slot service times, which leads to the introduction of two different service strategies depending on whether service of an interrupted customer continues or restarts after an interruption. For both alternatives, we establish expressions for the steady-state probability generating functions of the buffer contents, the unfinished work and the customer delay in terms of the effective customer service times. From these results, closed-form expressions for various performance measures, such as the moments of these quantities, can be established. After dealing with some stability issues, we illustrate the impact of both service strategies on the buffer performance with some numerical examples. 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.