Queuing Models with Lane Selection: A New Class of Problems

Abstract

This paper presents a new class of queuing models. There are n distinct types of customers and n distinct types of service facilities. Some customers can be processed at any service facility, but other customer types can only use selected ones among the service-facility types. This class of model is named “lane selection,” abbreviated LS, since the arriving customers with some freedom of choice must select the queue, or lane, in which they are to be processed through the system. It is shown by example that many physical situations are represented more accurately by this model than by more conventional ones. However, in analysis, the LS concept raises many theoretical difficulties. For a number of special cases, this paper obtains in explicit form as functions of the model parameters the mean queue lengths and waiting times for the different classes of customers.

Imaging Technologies in Aviation Security

“…Moreover, research by Schwartz shows that a freedom lane selection by passengers could work better than any conventional way. That led them to develop a static model to calculate the number of passengers and length of time at each lane depending on the class of passenger [47]. Recent research has developed a static simulation framework that makes use of the selected passenger lane depending on the neighborhood search procedure, which succeeded in the selection of 4% probability of true alarm than the usual passenger selection lane programme [48].…”

Analysis of the asymmetric shortest queue problem

“…Since the equations (2), (6) and (9) are linear, the linear combinations (27), (28) and (29) satisfy the equations (2), (6) and (9). This completes the formal definition of the numbers Xs,t and Xs,t for all s~0 and t~O.…”

“…The next step is to prove that the series (25), (26) and (29), which define Xs,t and Xs,t, converge absolutely. We need absolute convergence to guarantee (27) and (28). These series, however, do not necessarily converge absolutely for all s and t, but we will prove To prove that the series (25), (26) and (29) converge absolutely we need infonnation about the asymptotic behaviour of aj,~j, Cj and dj • Below we start to prove that aj and~j decrease exponentially fast, for which we need the following monotonicity result Lemma 4.…”

Time-Dependent Performance Approximation of Truck Handling Operations at an Air Cargo Terminal

“…Static routing decisions are analyzed by Ross and Yao [25], Ansell et al [2], Argon et al [3], and Liu and Righter [19]. In the case of state-dependent routing, threshold policies based on a particular facility may be applied (e.g., [26,28]) or routing decisions may be based on the state of several stations; e.g., an arriving job may be routed to the facility with the shortest queue (e.g., [6,1]). Furthermore, in contrast to our setting, all these references primarily restrict the scope of analysis to parallel single-server queues.…”