Dissertation committee:
Κυριακίδης Επαμεινώνδας, Καθηγητής, Τμ. Στατιστικής, Οικονομικό Πανεπιστήμιο Αθηνών
Μπουρνέτας Απόστολος, Καθηγητής, Τμ. Μαθηματικών, ΕΚΠΑ
Καραματσούκης Κωνσταντίνος, Αναπληρωτής Καθηγητής, Στρατιωτική Σχολή Ευελπίδων
Καναβέτας Οδυσσέας, Επίκουρος Καθηγητής, Mathematisch Instituut, Leiden Universiteit
Τρέβεζας Σάμης, Επίκουρος Καθηγητής, Τμ. Μαθηματικών, ΕΚΠΑ
Μάνου Αθανασία, Επίκουρη Καθηγήτρια, Τμ. Μαθηματικών, ΕΚΠΑ
Οικονόμου Αντώνιος, Καθηγητής, Τμ. Μαθηματικών, ΕΚΠΑ
Summary:
This Thesis deals with service systems under a game-theoretic framework where the customers and the system administrator can exhibit strategic behavior. Under this framework, the service systems are studied through an economic perspective, where the customers and the administrator are considered active entities that make decisions with economic considerations. These decisions are made to maximize their welfare, given the reward-cost structure of the system which from the customers' viewpoint, incorporates their desire for service and their unwillingness to suffer time delays due to congestion. Their decisions are also strategic, in the sense that individuals' beliefs about how others will decide, affect their decisions. Thus, the whole situation can be regarded as a game among the individual entities, where the primary objective is to determine the equilibrium strategy profiles and study its impact on the specific service system. On the other hand, the server administrator is a profit maximizer, who can control the service policy (allowing customers to renege or not), the provision of information (decide which level of information is the most appropriate) and regulate (implicitly) the customer flow through pricing.
In line with this framework, the dissertation consists of four distinct research projects, focusing on different aspects of strategic behavior and analyzing its impact on various service systems. Regarding the type of the strategic decisions, three different scenarios are investigated: the join-or-balk dilemma, the stay-or-renege dilemma, and the routing decisions, when several service options are available. We also study how these decisions are influenced by the provision of real-time information regarding several attributes of the system, as well as the impact of managerial decisions, such as to whether allow customers to renege or not. For these models, we provide a comprehensive game-theoretic and queueing analysis and discuss the equilibrium and socially optimal behavior.
In the first research project, we consider a general model of a transportation station where strategic customers arrive according to a Poisson process, the arriving instants of the transportation facilities form a renewal process and the capacities of successively arriving facilities are finite. Customers decide whether to stay or balk based on their expected waiting costs and the probability of being served, conditioning on the information provided. The information may include the capacity of the next facility, the elapsed time from the previous visit of the facility, and/or the number of customers that are present in the station. We derive the customer equilibrium strategies and compare the equilibrium throughput and social welfare, under various information structures. We then determine the ideal level of information that should be provided according to the operational and economic parameters of a given system.
\begin{sloppypar}Customer strategic behavior regarding the join-or-balk dilemma in queueing systems with server vacations/failures has been studied intensively in the recent literature. The standard assumption in these studies is that the joining customers are not allowed to renege later. In the second research project, we relax this assumption and quantify the value of reneging for strategic customers who face a queueing system with server vacations/failures. To focus on the reneging feature, we study the customer strategic behavior in the simplest such system, that is in the M/M/1 queue with a server alternating between on and off periods. We show that the possibility of reneging has a substantial effect on the equilibrium social welfare and throughput. In particular, as the reward from service varies in a given system, it becomes beneficial to activate or deactivate the option of reneging to ensure higher welfare. Moreover, we show that the effect of the reneging option is particularly significant in the case where the original system with non-strategic customers is unstable.
\end{sloppypar}
In the third research project, we consider the fluid on-off model of the basic queue with vacations/failures and study reneging vs. no-reneging when customers are strategic. We derive the equilibrium customer strategies and the corresponding performance measures of the system, and we use them to study the equilibrium throughput and social welfare. The main finding is that the existence of the reneging option is very beneficial for overloaded systems, i.e., for such systems balking alone is not sufficient to achieve good outcomes. On the contrary, for underloaded systems, the reneging option is not particularly valuable.
In the last research project, we study the routing decisions of passengers in a transportation station, where various types of facilities arrive with limited seating availability. The passengers’ arrivals occur according to a Poisson process, the arriving instants of the transportation facilities form independent renewal processes and the seating availability at the successive visits of the facilities correspond to independent random variables, identically distributed for each facility. We analyze the strategic passenger behavior and derive the equilibrium strategies. We also discuss the associated social welfare optimization problem.
Keywords:
Queueing, Strategic Behavior, equilibrium strategies, optimal policies, Join-Balk, Reneging, Routing
