Document Type : Original Article

Authors

• moein mohsenzadeh ¹
• Mahdi Doustparast ²
• Abdolrahim Badamchizadeh ³
• mohammad Jelodari Mamaghani ⁴

¹ Ph.D. student of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

² Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

³ Department of Statistics, Allameh Tabataba’i University, Tehran, Iran.

⁴ Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran

Abstract

This paper deals with a single unreliable server and with delaying vacations which has Poisson arrivals and general distribution for the service times. The server can be activated at arrival epochs or deactivated at service completion epochs. The maximum entropy principle is increasingly relevant to queueing systems. The principle of maximum entropy (PME) presents an impartial framework as a promising method to examine complex queuing processes. We use maximum entropy principle to derive the approximate formulas for the steady-state probability distributions of the queue length. The maximum entropy approach is then used to give a comparative perusal between the system’s exact and estimated waiting times. We demonstrate that the maximum entropy approach is efficient enough for practical purpose and is a feasible method for approximating the solution of complex queueing systems.

Keywords

• Maximum entropy
• M^([X])/G/1 queueing system
• delaying vacations
• un-reliable server