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1 2015

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Iterative Algorithm for Threshold Calculation in the Problem of Routing Fixed Size Jobs to Two Parallel Servers

Konovalov M., Razumchik R.

Journal of Telecommunications and Information Technology

2015

nr 3

32--38

At present, solutions of many practical problems require signicant computational resources and systems (grids, clouds, clusters etc.), which provide appropriate means are constantly evolving. The capability of the systems to full quality of service requirements pose new challenges for the developers. One of the well-known approaches to increase system performance is the use of optimal scheduling (dispatching) policies. In this paper the special case of the general problem of nding optimal allocation policy in the heterogeneous n-server system processing xed size jobs is considered. There are two servers working independently at constant but di erent speeds. Each of them has a dedicated queue (of innite capacity) in front of it. Jobs of equal size arrive at the system. Inter-arrival times are i.i.d. random variables with general distribution with nite mean. Each job upon arrival must be immediately dispatched to one of the two queues wherefrom it will be served in FCFS manner (no pre-emption). The objective is the minimization of mean job sojourn time in the system. It is known that under this objective the optimal policy is of threshold type. The authors propose scalable fast iterative non-simulation algorithm for approximate calculation of the policy parameter (threshold). Numerical results are given.