An Approach to Quality of Service

Abstract

Network Quality of Service (QoS) criteria of interest include conventional metrics such as throughput, delay, loss, and jitter, as well as new QoS criteria based on power utilization, reliability and security. In this paper we suggest a theoretical framework for the characterization and comparison of adaptive routing algorithms which use QoS as the criterion to select between different paths that connections may take from sources to destinations. Our objective is not to analyze QoS, but rather to provide routing rules which can improve QoS. We define a QoS metric as a non-negative random variable associated with network paths which satisfies a sub-additivity condition along each path. Rather than a quantity to be minimised (such as packet loss or delay), our QoS metrics are quantities that should be maximised (such as the inverse of packet loss or delay), similar in spirit to utility functions. We define the QoS of a path, under some routing policy, as the expected value of a non-decreasing measurable function of the QoS metric. We discuss sensitive and insensitive QoS metrics, the latter being dependent on the routing policy which is used. We describe routing policies simply as probabilistic choices among all possible paths from some source to some given destination. Sensible routing policies are then introduced: they take decisions based simply on the QoS of each available path. We prove that the routing probability of a sensible policy can always be uniquely obtained. A hierarchy of m-sensible probabilistic routing policies is then introduced and we provide conditions under which an (m+1)-sensible policy provides better QoS on the average than an m-sensible policy.