Sensible decisions based on QoS

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 data transmitted in the network (e.g. packets, connections, etc.) may take. Our objective is not to analyze QoS, but rather to design randomized routing policies which can improve QoS. We define a QoS metric as a non-negative random variables associated with network paths which satisfy a sub-additivity condition along each path. 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. Sensible policies, which make decisions based on the QoS of the paths, are introduced. 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 anm+1−sensible policy provides better QoS on the average than an m− sensible policy.