•  
  •  
 

Abstract

This research analyzed queuing system with encouraged arrivals under multiple working vacations and server breakdowns. It is based on a Mx/M/1 model, where the customers arrive in batches or bulk. In addition, the arrival follows a Poisson process and the service time is distributed exponentially. Moreover, in this queuing system, breakdowns can occur at any time, and it is affecting the server's service time. The repair time is independent. Server resume the service as soon as returns from the service facility. Repair time follows exponential distribution. Encouraged arrival in queuing models involves external factors or incentives that prompt the firms. This strategy for mitigating may include preventing maintenance or minimizing the service disruptions and maintain the system efficiency. Encouraged arrival in queuing model conscious effort to increase customers or other entities to a service system during specific periods. Encouraged arrival improves the system performance and service efficiency of the model. Finally, this research solved the Chapman-Kolmogorov balancing equations for the steady state system, analyzed the queuing model using probability generating function and discussed, the stochastic decomposition property and the expected system size.

Keywords

Breakdowns, Encouraged arrivals, Multiple working vacations, Probability generating function, Queuing system, Stochastic decomposition

Subject Area

Computer Science

First Page

740

Last Page

745

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Receive Date

5-31-2023

Revise Date

6-2-2024

Accept Date

6-4-2024

Download

Share

COinS