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Abstract:
We consider the path-determination problem in Internet core routers that distribute flows across alternate paths leading to the same destination. We assume that the remainder of the network transit delay beyond this router are different for the two paths, so a good routing policy can reduce the end-to-end delay by favoring the faster path. Thus, we propose and solve the optimal path-determination problem for a router, which minimizes the average network transit delay for a flow by dynamically assigning each packet to one of the available output ports based on their respective instantaneous queue lengths and on the average network transit delay for the associated path. We assume that all outgoing link speeds at the router are equal, but we generalize the model to allow each output port to serve a link group (such as an optical fiber using WDM) that consists of multiple physical channels running in parallel. By formulating path-selection as a Markov Decision Problem, we show that the optimal algorithm is a threshold-type policy that we call JSQ b.

Threshold routing, Markov decision process, Asymmetric paths, Virtual paths, Optical networks

Abstract:
We define a 'forking node' as a service centre with one input feeding two outputs (each served by its own queue) under the control of an internal path-selection (PS) policy. We assume that both outputs lead to paths through which a packet reaches its final destination. However, the mean downstream delays on the two paths may be different and the PS policy should favour the path with the lower downstream delay. Using simulation, we compare the performance of this system under a variety of random, deterministic, state-dependent PS policies, including threshold-based and join-shortest-queue with bias (JSQ + b). We show that JSQ + b has better performance than the other alternatives. Moreover, if the input process to the forking node is Poisson, standard time series analysis techniques show that its two outputs are very close to being independent Poisson processes. Thus, if we find an accurate and efficient 'offline' analytical performance model for JSQ + b forking node, we can extend the applicability of product-form queueing networks to include such forking nodes. For this reason, we present several ways of modelling the performance of a JSQ + b node, using bounds, and compare their results on example networks. We establish a closed-form expression relating the bias b and the delays of the downstream paths.

asymmetric networks, parallel servers, path selection policy, performance bounds