Mathematics and Statistics Vol. 11(4), pp. 654 - 660
DOI: 10.13189/ms.2023.110406
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A New Type of Single Server Queue Operating in A Multi-level Environment with Customer Impatience

Akshaya Ramesh , S. Udayabaskaran ^*
Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, India

ABSTRACT

A new type of single server queue is considered. In this type, the server asks for an assignment in a multi-level environment and the customer develops impatience during the assignment process. The environment has N levels and the server is assigned to operate in one of these levels with level dependent arrival and service rates. Customers arrive at the system all the time and there is an infinite buffer with the system. The assignment is done by a random switch which can initiate an assignment process only if at least one customer is in the system. The server working in any level of the environment reports to the random switch after serving the last customer in that level. Customers are not flushed out at any time. The random switch initiates an assignment process immediately at the epoch of arrival of a customer to the system. Assignment time is random and during the assignment period, customers are permitted to join the system. Once the assignment process starts, each customer waiting in the buffer clicks on a random impatience timer with him/her and leaves the system in case his/her timer ends before the assignment to the server is made. For this model, steady-state probabilities are found and a performance analysis is also made.

KEYWORDS
Single Server Queue, Multi-level Environment, Assignment, Random Switch, Customer Impatience

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Akshaya Ramesh , S. Udayabaskaran , "A New Type of Single Server Queue Operating in A Multi-level Environment with Customer Impatience," Mathematics and Statistics, Vol. 11, No. 4, pp. 654 - 660, 2023. DOI: 10.13189/ms.2023.110406.

(b). APA Format:
Akshaya Ramesh , S. Udayabaskaran (2023). A New Type of Single Server Queue Operating in A Multi-level Environment with Customer Impatience. Mathematics and Statistics, 11(4), 654 - 660. DOI: 10.13189/ms.2023.110406.