A first passage time problem for spectrally positive Lévy processes and its application to a dynamic priority queue

We study a first passage time problem for a class of spectrally positive Lévy processes. By considering the special case where the Lévy process is a compound Poisson process with negative drift, we obtain the Laplace–Stieltjes transform of the steady-state waiting time distribution of low-priority customers in a two-class M/GI/1 queue operating under a dynamic non-preemptive priority discipline. This allows us to observe how the waiting time of customers is affected as the policy parameter varies

Managing Perishability in Service Operations

We study three problems in service operations where either the supply or demand is perishable. In the first chapter, we study a perishable inventory system for items whose quality deteriorates in time, e.g., blood products. Specifically, we assume that supply and demand are driven by independent Poisson processes, units have a constant shelf-life, and unsatisfied demand is lost. We consider a threshold-based allocation policy that trades off the age and availability of allocated units. We characterize the sojourn time distribution of units in inventory and evaluate the performance of the threshold policy in terms of the distribution of the age of allocated units and the proportion of outdates and lost demand. Our numerical results demonstrate the importance of system parameters on the performance of the policy and identify important properties of the distribution of the age of allocated units. In the second chapter, we study the performance of certain practical ordering and allocation policies in reducing the age of transfused blood in hospitals while keeping the outdate and shortage rates low. We develop a data-driven (evidence-based) simulation model based on the operations of the blood bank of an acute care hospital in Hamilton, Ontario. We use empirical data to validate our model and estimate its inputs. The results suggest that by properly adjusting the ordering and allocation policies at the hospital level, a significant reduction of issue age could be achieved, without compromising availability or resulting in excessive outdates. In the third chapter, we study the rational abandonment behavior of utility-maximizing customers in the context of an observable priority queue, and identify novel pricing implications. We first characterize the equilibrium abandonment strategy of low-priority customers. We then consider pricing as a means to control the abandonment behavior and investigate its implications on system welfare and firm revenue. A distinguishing feature of our model is that in the presence of abandonment the timing of payment matters. We show that the welfare can be maximized using only a single fee charged upon service completion. In contrast, revenue maximization generally requires a combination of both an entrance and a service fee.Ph.D

Certain Static and Dynamic Priority Policies in Queueing Systems

In this thesis, we first study delay systems with different classes of impatient customers. We analyze the M/GI/1+M queue serving two priority classes under the static non-preemptive priority discipline. We also study the multi-server priority queue considering two cases depending on the time-to-abandon distribution being exponentially distributed or deterministic. In all models, we obtain the Laplace transforms of the virtual waiting time for each class by exploiting the level-crossing method. This enables us to obtain the steady-state system performance measures. In the second part, we consider the steady-state waiting time distributions of a two class M/GI/1 queue operating under a dynamic priority discipline. We find an accurate approximation for the steady-state waiting time distribution of the low-priority customers which allows us to study how they are penalized as the priority parameter increases. We also obtain bounds for the variance of the waiting time of high-priority customers.MAS

Optimizing inspection strategies for multi-stage manufacturing processes using simulation optimization

This paper deals with the problem of determining the op-timal inspection strategy for a multi-stage production process using simulation optimization. An optimal inspec-tion strategy is the one that results in the lowest total in-spection cost, while still assuring a required output qual-ity. Because of the complexity of the problem, simulation is used to model the multi-stage process subject to inspec-tion and to calculate the resulting inspection costs. Simu-lation optimization is then used to find the optimal inspec-tion strategy. The performance of the proposed method is presented through the use of a numerical example.

Waiting time analysis of multi-class queues with impatient customers

In this paper, we study three delay systems where different classes of impatient customers arrive according to independent Poisson processes. In the first system, a single server receives two classes of customers with general service time requirements, and follows a non-preemptive priority policy in serving them. Both classes of customers abandon the system when their exponentially distributed patience limits expire. The second system comprises parallel and identical servers providing the same type of service for both classes of impatient customers under the non-preemptive priority policy. We assume exponential service times and consider two cases depending on the time-to-abandon distribution being exponentially distributed or deterministic. In either case, we permit different reneging rates or patience limits for each class. Finally, we consider the first-come-first-served policy in single and multi-server settings. In all models, we obtain the Laplace transforms of the virtual waiting time for each class by exploiting the level-crossing method. This enables us to compute the steady-state system performance measures