This paper deals with the difficult problem of calculating the waitingtime probabilities in the M/G/1 queue with retrials. The waiting-time distribution is approximated by a gamma distribution by matching the first two moments. Numerical results indicate that this approximation performs satisfactory for practical purposes.
A practically important problem is the assignment of stochastically arriving service requests to one of several parallel service groups so as to minimize the long-run average sojourn time per service request. An exact solution of this multi-dimensional optimization problem is computationally infeasible.A simple heuristic solution method yielding a good suboptimal rule will be given for the case of server groups with different and generally distributed service times. This solution method is based on a decomposition approach and first principles from Markov decision theory. The main idea of the heuristic method is to apply one step of policy improvement to the best Bernoulli-splitting rule.
This paper considers a queueing model with batch Poisson input and two heterogeneous servers, where the service times are exponentially distributed. The faster server is always on, but the slower server is only used when the queue length exceeds a certain level. Activating the slower server involves fixed set-up costs. Also there are linear operating costs and linear holding costs. The class of two-level hysteretic control rules is considered. Rather than proving the overall average cost optimality of a hysteretic rule, the purpose of this paper is to develop a tailor-made policyiteration algorithm for computing the optimal switch-on and switch-off levels for the slower server. An embedding method is used that is generally applicable to structured Markovian control problems with an infinitely large state space.Index Terms-Controlled queueing system, heterogeneous servers, Markov decision theory.
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