Resource Availability Modeling and Optimization in a Car Park Management Problem

Abstract

This paper addresses the modeling and optimization of resource availability in car parks, serving different priority classes of customers. The authors examine various formulations of the problem concerning two general objectives: a) increasing the availability for high priority customers and b) maximizing the aggregate service level. In the current context, priority classes are specified according to different space reservation options provided by the parking management company (monthly parking, hourly parking, parking on demand, etc.). Based on actual historical traffic data and under certain methodological assumptions, they calculate the arrival and service rates for each class of customers. These are subsequently used as inputs in a Markov model that describes the evolution of the number of free parking spaces in time, given that some spaces are reserved for higher priority classes. Optimization techniques and OR heuristics are applied to deal with numerical aspects of the associated reservation planning issues.

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

“…k−1,s denoting the reserved resources that can be accessed only by clients of Class 1 in P1. Note that g 1 1,s are the parking places that are reserved for clients of Classes 1 to k − 1 in P1, g 1 2,s are the corresponding reserved places that can be accessed by clients of Classes 1 to k − 2 and so on. In general, g 1 m,s for 1 ≤ m ≤ k − 1 denotes the parking places that are reserved for clients of Classes 1 to k − m. All the arriving clients independently of their class are accepted in P1 until the number of free places in P1 reduces to ∑ k−1 m=1 g 1 m,s .…”

“…The main idea of this technique lies on the fact that a number of resources are reserved for priority classes of clients, though the rest of the resources can be offered not only to priority clients but to any client too. Resource reservation is widely used for guarding cells in cellular networks, 1 for server resources, 8 for website resources, 12,13 for reserving mailmen for urgent deliveries in courier services, 15 for distributed multi-path quality of service routing, 21 for enhancing the end-to-end performance of network applications, 22 for cloud computing resources, 23 and for reserving parking places. 1,24,25 Enabling resource reservation to achieve a trade-off, aims in optimizing the probability of finding an available parking place for each client class.…”

“…For example, a client who pays a monthly fee is of higher priority for the company than a client who incidentally decides to use a certain parking lot and may not visit it ever again. 1 Priority in this case means that the company is somehow obligated to provide a parking place to its monthly clients no matter what, and any free places remaining can be offered to incidental clients. Such a policy can be usually achieved by reserving an amount of parking places for clients with higher priorities.…”

“…The later probability is called blocking probability. 1,[26][27][28] Providing QoS to all clients presupposes that blocking probabilities for all classes must be minimized simultaneously. To do this, optimization techniques need to be adopted with respect to the resource reservation policy.…”

“…Resource reservation is widely used for guarding cells in cellular networks, 1 for server resources, 8 for website resources, 12,13 for reserving mailmen for urgent deliveries in courier services, 15 for distributed multi-path quality of service routing, 21 for enhancing the end-to-end performance of network applications, 22 for cloud computing resources, 23 and for reserving parking places. 1,24,25 Enabling resource reservation to achieve a trade-off, aims in optimizing the probability of finding an available parking place for each client class. In other words, an appropriate resource reservation policy is a policy that manages to minimize the probability of denial of service for each priority class due to parking places unavailability.…”