Reducing Customer Abandonment Through the Characteristic Function of Two Queueing Games with Exponential Reneging
Author(s):
D. Dutta
D. Dutta
Department of Science & Humanities (Mathematics)
National Institute of Technology Nagaland
Chumukedima, Nagaland
India.
deepraj.dutta299@gmail.com
0009-0002-6608-7762
,
M. K. Patel
M. K. Patel
Department of Science & Humanities (Mathematics)
National Institute of Technology Nagaland
India.
Chumukedima, Nagaland
India.
mkpitb@gmail.com
0000-0003-1010-261X
Abstract
Customer abandonment, also known as reneging, is a major problem for queueing systems. A high amount of reneging in a queueing system leads to reduced goodwill for the system. Queueing systems therefore aim to reduce reneging. Reneging is therefore modeled as a cost on the queueing system. In this paper, we propose a cooperative game theoretic approach to solve the problem of reneging in queueing systems with Poisson arrival, exponential service times and exponential reneging. We define two aggregation principles. These two aggregation principles give us two types of cooperative games. We consider the characteristic function as the average reneging rate in both games. We establish an inequality between the values of the characteristic functions of the two games. Subadditivity of the games is explored using random sampling. Furthermore, a differential evolution algorithm is used to find the non-emptiness of the core in both games. Finally, we use numerical illustrations to demonstrate the cost reduction that can be achieved using the two different aggregation principles. The nucleolus is used for distributing the cost of the grand coalition. The cost of reneging for each player in game one is compared with the cost for that player in game two.
Keywords
Poisson arrival, Exponential service, Level dependent reneging, Differential evolution algorithm.
2020 Mathematics Subject Classification
90B22, 60K25, 91A12, 68W50, 60J28.