Entropy Analysis of a Flexible Markovian Queue with Server Breakdowns

Entropy

Ramdane Hedjar¹  Lotfi Tadj²  Messaoud Bounkhel³ 

[1] Department of Computer Engineering, King Saud University, Riyadh 11453, Saudi Arabia;Department of Industrial Engineering, Alfaisal University, Riyadh 12714, Saudi Arabia;Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia;

关键词: Markovian queue;    flexible server;    unreliable server;    steady-state distribution;    maximum entropy principle;   

DOI  :  10.3390/e22090979

来源: DOAJ

【 摘 要 】

In this paper, a versatile Markovian queueing system is considered. Given a fixed threshold level c, the server serves customers one a time when the queue length is less than c, and in batches of fixed size c when the queue length is greater than or equal to c. The server is subject to failure when serving either a single or a batch of customers. Service rates, failure rates, and repair rates, depend on whether the server is serving a single customer or a batch of customers. While the analytical method provides the initial probability vector, we use the entropy principle to obtain both the initial probability vector (for comparison) and the tail probability vector. The comparison shows the results obtained analytically and approximately are in good agreement, especially when the first two moments are used in the entropy approach.

【 授权许可】

Unknown