Due-date setting and priority sequencing in a multiclass M/G.1 queue
Management Science
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
ACM Transactions on Mathematical Software (TOMS)
Single facility due date setting with multiple customer classes
Management Science
Management Science
Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform
Journal of the ACM (JACM)
Algorithm 368: Numerical inversion of Laplace transforms [D5]
Communications of the ACM
Interdeparture time distributions in ΣiMi/Gi/1 priority queues
Queueing Systems: Theory and Applications
A Unified Framework for Numerically Inverting Laplace Transforms
INFORMS Journal on Computing
Power Algorithms for Inverting Laplace Transforms
INFORMS Journal on Computing
Waiting and sojourn times in a multi-server queue with mixed priorities
Queueing Systems: Theory and Applications
Dynamic Lead-Time Quotation for an M/M/1 Base-Stock Inventory Queue
Operations Research
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We discuss the evaluation of expected tardiness of an order at the time of arrival in an M/M/c queuing system with N priority classes, considering both nonpreemptive and preemptive service disciplines. Upon arrival, a customer order is quoted a lead time of d, and placed in the queue according to the priority class of the customer. Orders within the same priority class are processed on a first-come, first-served basis. We derive the Laplace transforms of the expected tardiness of the order given the quoted lead time, priority class of the order, and system status. For the special case of single priority class, the Laplace transform can be inverted into a closed-form expression. For the case with multiple priority classes, a closed-form expression cannot be obtained, hence, we develop three customized numerical inverse Laplace transformation algorithms. Two of these algorithms provide upper and lower bounds for the expected tardiness under a simple condition on system parameters. Using this property, we obtain error bounds for our customized algorithms; such bounds are not available for general purpose numerical inversion algorithms in the literature. Next, we develop a novel methodology to compare the precision of general purpose numerical inversion algorithms and analyze the performances of three algorithms from the literature. Finally, we provide a recommendation scheme given computational time and error tolerances of the decision maker. The methods developed in this paper for the accurate estimation of expected tardiness establish an important step toward developing due date quotation policies in a multiclass queue, contributing to the due date quotation literature that has been largely focused on single-class queues.