On a Queueing-Inventory Problem in Passenger Transport System

• Published in: Distributed Computer and Communication Networks pp. 215 - 229
• Main Authors: Shajin, Dhanya, Jacob, Jaison, Vishnevskiy, V. M., Krishnamoorthy, A.
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing
• Series: Communications in Computer and Information Science
• Subjects: Common life time; Overbooking; Schedule cancellation
• ISBN: 9783030366247; 3030366243
• ISSN: 1865-0929; 1865-0937
• DOI: 10.1007/978-3-030-36625-4_18

We consider a queueing-inventory problem arising in transport of passengers (flight/train/bus) in which seats in the passenger vessel are assumed to be physically available inventory. Two types of customers – type 1 (high priority (HP)) and type 2 (low priority (LP)) arrive for service. High priority customers have a finite buffer to wait whose maximum capacity is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S+V$$\end{document}, where S is the capacity of the vessel and V is the number of overbookings permitted. Low priority customers wait in an infinite capacity queue. High priority customers have non-preemptive priority over low priority customers. Arrival of customers form a marked Poisson process. Service time for each customer is exponentially distributed. Each customer asks for exactly one item from inventory which requires an exponentially distributed time for processing (reservation). The service time parameter varies with the “stage of common life time of items for reservation”. Vehicle departure time is regarded as “realization of common life time (CLT) of seats in the vehicle”. To be precise, inter departure time of vehicles is assumed to have Erlang distribution with K stages. Instantly the next vessel is scheduled. In addition to advanced reservation of seats (inventory), those customers who already reserved seats can “cancel their reservation”, before CLT gets realized. Depending on the number of overbookings, the vessel capacity for the scheduled departure is modified (for example, a larger vessel is employed if the number of overbooking at the time of departure is high enough; else the normal vessel is used). We derive the stability condition for the system. Then we go about computing the system state distribution. From these we derive expressions for computing performance of the system. Finally we analyze an optimization problem associated with the model.