Analysis of Tollbooth Systems with Two Tandem Skill-Based Servers and Two Vehicle Types

• Published in: Methodology and computing in applied probability 2020-09, Vol.22 (3), p.1145-1167
• Main Authors: Chang, Baoxian, Jiang, Tao, Ye, Qingqing, Chai, Xudong, Liu, Liwei
• Format: Article
• Language: English
• Subjects: Business and Management; Closed form solutions; Economics; Electrical Engineering; Exact solutions; Life Sciences; Mathematics and Statistics; Queues; Statistics; Vehicles
• ISSN: 1387-5841; 1573-7713
• DOI: 10.1007/s11009-019-09758-w

The existing tollbooth systems with multi-type vehicles in transportation literature typically assume the servers are either dedicated for each vehicle type or generic for all vehicle types. Conversely, in this paper, we focus on studying two similar systems both with skill-based servers, i.e., each tollbooth can handle a given subset of vehicle types. Meanwhile, we assume that vehicles queue together in a single lane, thus they get served by global First-Come-First-Served discipline. The slight difference between these two systems is the number of exits: one with a single exit (model 1) and the other with two exits (model 2). Nevertheless, it creates large difference in the resolving process. By spectral expansion technique, we obtain a closed-form solution for the system’s steady-state probabilities in the former model and the explicit solution without closed-form expressions in the latter model. By numerical results, we demonstrate how the parameters selection influences system’s performance, along with some intriguing managerial insights. We also use the system of the same structure but with dedicated servers as the baseline for comparisons to show the benefits of skill-based servers.