Multiple depot inventory systems with stock transfer are used by many companies especially when demand is high relative to storage capacity. The key issues in such systems are how many of each item to hold at each depot and what to do if there is a demand for an item at a depot that has none of that item in stock. This study was motivated by the inventory problem faced by a UK car part retailer that groups its depots into pairs. The company's policy for dealing with a demand at a depot that cannot be satisfied from local stock is to either transfer the item from the other depot in the group or to place an emergency order. The object of this paper is to characterise an optimal policy for this problem and to propose a method of calculating the parameters of such a policy.inventory systems, Markov decision models, dynamic programming

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.

A transaction scheduling mechanism is designed for a shared-memory, m ulti-processor database system. The scheduler used is a variant of static locking, adapted for real-time and more than one processor.It is assumed that transactions arrive according to a Poisson process, execution times of transactions are independent and exponentially distributed, and all transactions use the same number of data items. The system is then represented as a Markov model. A steady state is derived from this model. By examining the path through the system of a single transaction, a recursive relation that describes all moments of a transaction's response time is derived. The moments are obtained from this relation with dynamic programming.The response time distribution is approximated by tting a distribution to the rst two moments. Simulation shows that this approximation gives excellent results.

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The MaGaI queue with Optimistic Concurrency Control (OCC) is a model for a special form of parallel transaction processing in a real-time database. Transactions arrive according to a Poisson process and require some generally distributed execution time. One of the differences with ordinary multi-and in®nite-server queueing models is that under OCC the successful completion of one transaction may immediately cause the failure of one or more of the other transactions. This happens if the completing transaction has overwritten a data-item that is in use by another transaction in progress. As soon as this failure is detected the failed transaction is restarted. So the total service time of a transaction consists of its ®nal successful run and the time spent on unsuccessful runs.In this study we develop an approximation for the distribution of the total service time, and test the approximation against simulation. Although in practice the number of servers is never unlimited, this study provides valuable insight in the asymptotics with respect to the number of servers. The approximation clearly demonstrates the very limited performance gain from an increase of the number of servers.