We study the workload (unfinished work) and the waiting time of the queueing system with MAP arrivals under D-policy. The D-policy stipulates that the idle server begin to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We first set up the system equations for workload and obtain the steady-state distributions of workloads at an arbitrary idle and busy points of time. We then proceed to obtain the waiting time distribution of an arbitrary customer based on the workload results. The M/G/1/D-policy queue will be investigated as a special case.

Workload and Waiting Time Analyses of MAP/G/1 Queue under D-policy

We study the queue length distribution of a queueing system with MAP arrivals under D-policy. The idle server begins to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We derive the vector generating functions of the queue lengths both at a departure and at an arbitrary point of time. Mean queue lengths will be derived from these transform results. A numerical example is provided.

Queue Length Analysis of MAP/G/1 Queue Under D-Policy

We consider the preventive maintenance of a production system that is deteriorated by random shocks and the production process itself. The degree of deterioration is modeled by discrete and finite states. Shocks arrive according to a Poisson process and deteriorate the system by random amounts. The system may deteriorate whenever it produces an item. The system is continuously monitored and repaired if the system state is at or above a predetermined level for maintenance. We analyze the lifetime, product quantity, average cost, and average profit considering revenue from the product and cost due to setup, operation, and repair. Assuming a structure of system parameters and costs, using numerical examples, we investigate the impact of production and shock arrivals on the average profit and the optimal maintenance level that maximizes the average profit. The proposed model is applicable to manufacturing tasks in which machines wear due to production, for example, press processes, milling, turning, punching, and drilling.

Maintenance of multi-state production systems deteriorated by random shocks and production

The performance of the M/G/1 queue under the dyadic Min(N,D)-policy and its cost optimization

We study the queue length of the M X /G/1 queue under D-policy. We derive the queue length PGF at an arbitrary point of time. Then, we derive the mean queue length. As special cases, M/G/1, M X /M/1, and M/M/1 queue under D-policy are investigated. Finally, the effects of employing D-policy are discussed.

Analysis of the Mx/G/1 queue under D-policy

Instead of using the expected unfinished work, we use the expected number of customers in the system for finding the optimal D-policy for the M/G/1 queue in order to make it consistent with other control policies such as N-policy and T-policy.

On the Optimal D-Policy for the M/G/1 Queue

Correction and addendum : analysis of unfinished work and queue waiting time for the m/g/1 queue with d-policy

Analysis of Unfinished Work and Queue Waiting Time for the M/G/1 Queue with D-policy

We present a transform–free analysis of the following model. The state of the system is initially 0 and thereafter increases jumpwise due to compound Poisson shocks. Each shock increases the state by a random amount. The system is inspected at random points in time. If the state is above a threshold at an inspection, the system is replaced, otherwise no action is taken. Each replacement instantaneously brings the state back to 0. (Existing models assume either exponential interinspection times or discrete shock magnitudes.) This model can be applied to reliability, inventory, and queueing problems.Interpretations are given throughout to make the results easier to understand and to apply

Yon-Il Park

Papers

On the Optimal D-Policy for the M/G/1 Queue

Correction and addendum : analysis of unfinished work and queue waiting time for the m/g/1 queue with d-policy

Analysis of Unfinished Work and Queue Waiting Time for the M/G/1 Queue with D-policy

A random review replacement model for a system subject to compound poisson shocks