A cyclic non‐homogeneous Markov chain model for resource availability optimization in a two‐parking lots system with priority classes and resource reservation

Abstract

AbstractResource availability optimization has gained a lot of research effort recently, especially in client–server systems. A parking lot can be considered such a client–server system. Parking lot resource availability importance increased during the last decades since there is a tremendous increase of vehicles' usage not only in urban areas but in rural areas too. Academia and industry have extensively studied the problem of parking availability under various constraints and limitations. In this article, we extend previous work on parking lot resource availability optimization by providing an integrated theoretical framework for modeling resource reservation in a two‐parking lot problem which can be accessed by clients of different priorities under nonconstant arrival and service rates. The aim is to determine the optimal parking place reservation policy, which minimizes the blocking probability for each clients' class at each parking lot for different traffic periods. Under the optimal policy, we compute two different performance indicators; from clients' perspective we compute the total expected walking time from the parking lot to the point of interest, and from company's point of view, the total expected hourly profit. To model the fact that clients' arrival and service rates are time dependent, we use a cyclic nonhomogeneous Markov chain to model the entire system's evolution in time. Additionally, an empirical numerical case study is provided to examine the effectiveness of the proposed resource reservation approach.