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We consider a broad class of communication tasks, which we call isotropic, in a hypercube and in a wraparound mesh of processors. These tasks are characterized by a type of symmetry with respect to origin node. WVe show that executing such tasks in a minimum number of steps is equivalent to a matrix decomposition problem. We use this property to obtain minimum completion time algorithms. For a special communication task, the total exchange problem, we find algorithms that are simultaneously optimal with respect to completion time, and average packet delay. We also prove that a particularly simple type of shortest path algorithm executes isotropic tasks in time which is optimal within a small bound.

We analyze circuit switching in a multiprocessor network, where connection requests (or sessions) arrive at each node of the network according to a Poisson process with rate 1. Each session joins the appropriate input-queue at its source node, and, upon advancing to the head of the queue, transmits a setup packet to establish a connection. If the setup packet is successful, it reserves the links on the path for the duration of the session, and the session is served without interruptions. Otherwise, the connection request remains queued at the source, and subsequent attempts are made to establish the circuit. We analyze the queue of connection requests at the input-buffer of a network link, and obtain analytic expressions for the stability region, the average queuing delay, the average connection time, the average waiting time, and the average total delay, which show how these parameters depend on system variables, such as network dimension and session arrival rate. The queuing analysis focuses on the input-queue of a particular link, and accounts for the interactions with queues of other links through the retrial attempts and the associated probability of success. The queuing analysis is independent of the particular network topology under consideration, as long as the probability that a session arriving at a random time successfully establishes a connection can be calculated for that network. Simulations demonstrate the close agreement between the observed network behavior and that predicted by the analysis.

We consider the problem where broadcast requests are generated at random time instants at each node of a multiprocessor network. In particular, in our model packets arrive at each node of a network according to a Poisson process, and each packet has to be broadcast to all the other nodes. We propose an on-line decentralized routing scheme to execute the broadcasts in this dynamic environment. A related, although static, communication task is the partial multinode broadcast task, where M < N arbitrary nodes of an N-processor network broadcast a packet to all the other nodes. The results that we obtain for the dynamic broadcasting scheme apply to any topology, regular or not, for which partial multinode broadcast algorithms with certain properties can be found. For the dynamic scheme we find an upper bound on the average delay required to serve a broadcast request, and we evaluate its stability region. As an application we give a near-optimal partial multinode broadcast algorithm for the hypercube network. The stability region of the corresponding hypercube dynamic scheme tends to the maximum possible as the number of nodes of the hypercube tends to infinity. Furthermore, for any fixed load in the stability region, the average delay is of the order of the diameter of the hypercube.

This paper presents results from the IST Phosphorus project that studies and implements an optical Grid test-bed. A significant part of this project addresses scheduling and routing algorithms and dimensioning problems of optical grids. Given the high costs involved in setting up actual hardware implementations, simulations are a viable alternative. In this paper we present an initial study which proposes models that reflect real-world grid application traffic characteristics, appropriate for simulation purposes. We detail several such models and the corresponding process to extract the model parameters from real grid log traces, and verify that synthetically generated jobs provide a realistic approximation of the real-world grid job submission process.

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