Sensible decisions based on Quality of Service

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. Variable and adaptive routing have again become of interest in networking because of the increasing importance of mobile ad-hoc networks. In this paper we develop a probability model of adaptive routing algorithms which use the expected QoS to select paths in the network. Our objective is not to analyze QoS, but rather to design randomized routing policies which can improve QoS. We define QoS metrics as 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. Incremental routing policies are defined as those which can be derived from independent decisions taken at certain points (or nodes) along paths. 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. A 0-sensible policy is simply a random choice of routes with equal probability, while a 1-sensible policy selects a path with a probability which is inversely proportional to the (expected) QoS of the path. We prove that an m + 1-sensible policy provides better QoS on the average than an m-sensible policy, if the QoS metric is insensitive. We also show that under certain conditions, the same result also holds for sensitive QoS metrics.