Statistics Seminars: Greedy server on Z^1 (revisited)
5 December 2016 14:00 in CM221In this talk we will consider the problem of the behaviour of a greedy server on Z^1 initially considered by Kurkova and Menshikov. We will consider the following model where we have a queue of customers at each point, N \in Z^1, fed by a Poisson process of rate \lambda. There is a single server which serves the queue associated with the point of it’s current location, service times are exponentially distributed mean 1/\mu, until that queue is empty. The server then compares the queue length of the two neighbouring queues and moves at speed 1 towards the point with the longest queue length. We are then interested in the behaviour of the location of the server and whether the server’s location is recurrent or transient. Initially we will review the previously obtain results for \mu<\lambda and \mu>\lambda and known results for the related continuous model. Then we will examine progress which has been made on understanding the open case of lambda=mu as well as a propose a number of possible further extensions to probe the transitions between the different behaviours. This is ongoing work with Andrew Wade.
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