Optimal service-rate control of M/G/1 queueing systems using phase methods

A new approach to the optimal control of the service rate in M/G/1 queues is introduced using the method of phases. Each customer's work requirement is approximated by a random number of exponential phases with (possibly) different parameters (a generalized hyper-Erlang distribution). Using a semi-Markov decision-process formulation, we establish monotonicity properties of optimal policies for the finite-horizon problem, by induction on the horizon length. The analysis is then extended to the discounted infinite-horizon and the long-run average-return problems. In contrast to the models in previous papers, our model is appropriate for situations where the system controller has partial information about the work requirement of a customer, specifically the number of phases (tasks) to be performed. Because it requires a multidimensional state description, the analysis of the phase-type control model may be viewed as a first step toward the solution of control models for networks of queues.

Optimal service-rate control of M/G/1 queueing systems using phase methods

A new approach to the optimal control of the service rate in M/G/1 queues is introduced using the method of phases. Each customer's work requirement is approximated by a random number of exponential phases with (possibly) different parameters (a generalized hyper-Erlang distribution). Using a semi-Markov decision-process formulation, we establish monotonicity properties of optimal policies for the finite-horizon problem, by induction on the horizon length. The analysis is then extended to the discounted infinite-horizon and the long-run average-return problems. In contrast to the models in previous papers, our model is appropriate for situations where the system controller has partial information about the work requirement of a customer, specifically the number of phases (tasks) to be performed. Because it requires a multidimensional state description, the analysis of the phase-type control model may be viewed as a first step toward the solution of control models for networks of queues.

Applying the method of phases in the optimization of queuing systems

A new device in the optimization of queuing systems is introduced by using the method of phases. Non-exponential queues under control are considered with respect to the expected discounted reward criterion. For models with hyper-Erlang distributions equivalent phase-type systems are established. Approximation results for Markov decision models allow the extension to the case of general distribution functions. The approach is demonstrated by finding the form of an optimal policy for the GI/M/c queue with customer admission and batch arrival as well as for the GI/M/1 queue with interarrival time control.

Applying the method of phases in the optimization of queuing systems

A new device in the optimization of queuing systems is introduced by using the method of phases. Non-exponential queues under control are considered with respect to the expected discounted reward criterion. For models with hyper-Erlang distributions equivalent phase-type systems are established. Approximation results for Markov decision models allow the extension to the case of general distribution functions. The approach is demonstrated by finding the form of an optimal policy for the GI/M/c queue with customer admission and batch arrival as well as for the GI/M/1 queue with interarrival time control.

On the work load process in a general preemptive resume priority queue

Consider the following queuing system: A sequence of customers arrive at a service unit in a recurrent stream. A customer is of priority k with probability πk , k = 1, …, n. A class i customer preempts service of class k, k > i. Interrupted service is resumed without loss or gain in service time. Service is FIFO within classes. Service times for class k are drawn from a general distribution function Bk (t). Using the method of phases and a resolution technique from the theory of Markov processes we obtain Laplace transforms of various distributions.

On the work load process in a general preemptive resume priority queue

Consider the following queuing system: A sequence of customers arrive at a service unit in a recurrent stream. A customer is of priority k with probability πk, k = 1, …, n. A class i customer preempts service of class k, k > i. Interrupted service is resumed without loss or gain in service time. Service is FIFO within classes. Service times for class k are drawn from a general distribution function Bk(t).Using the method of phases and a resolution technique from the theory of Markov processes we obtain Laplace transforms of various distributions.