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Extrapolation of an Optimal Policy using Statistical Probabilistic Model Checking

Rataj A., Woźna-Szcześniak B.

Fundamenta Informaticae

2018

Vol. 157, nr 4

443--461

We present different ways of an approximate extrapolation of an optimal policy of a small model to that of a large equivalent of the model, which itself is too large to find its exact policy directly using probabilistic model checking (PMC). In particular, we obtain a global optimal resolution of non-determinism in several small Markov Decision Processes (MDP) or its extensions like Stochastic Multi-player Games (SMG) using PMC. We then use that resolution to form a hypothesis about an analytic decision boundary representing a respective policy in an equivalent large MDP/SMG. The resulting hypothetical decision boundary is then statistically approximately verified, if it is locally optimal and if it indeed represents a “good enough” policy. The verification either weakens or strengthens the hypothesis. The criterion of the optimality of the policy can be expressed in any modal logic that includes a version of the probabilistic operator P~p[·], and for which a PMC method exists.

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.