Optimal Control of Queueing Systems with Variable Number of Exponential Servers

摘要

A general switching cost model is formulated, and the problem of characterizing the optimal policy for a certain class of systems possessing such a cost structure is addressed. The class of systems studied can be described in terms of a pair of state descriptors which render the underlying probabilistic structure Markovian. The state descriptor consists of a one-dimensional variable, called exogenous, which is subject to explicit control by the decision-maker, and a vector of variables, called endogenous, which are only implicitly controlled by the decision-maker. The variable server M/M/c queueing system is an example. In such a system the exogenous variable is the number of servers employed (bounded above by c), and the endogenous variable is the number of customers in the system. The cost structure consists of two components: a variable cost of the system being in a particular state, assumed to be proportional to the length of time spent in that state, and a switching cost incurred instantaneously whenever the value of the exogenous variable is changed. A framework is developed for the analysis of systems where the length of time between review points is a random variable dependent on the state of the system. A characterization of the optimal control policy is given. The M/M/c queueing system is considered in detail and some attention is also given to the GI/M/c queueing system.