A discrete time queueing system with negative customers and single working vacation

Author

Jia, Songfang ; Chen, Yanheng

Author_Institution

Coll. of Math. & Comput. Sci., Chongqing Three Gorges Univ., Chongqing, China

Volume

4

fYear

2011

fDate

11-13 March 2011

Firstpage

15

Lastpage

19

Abstract

In this paper, we analyze a discrete time queueing system with geometrical arrivals of both positive and negative customers in which the server works at a lower rate during working vacation. Using embedded Markov chain and the matrix analysis solution method, we derive the probability generating function (PGF) of the number of customers waiting in the system and stationary queue length. From the process of the proof and the results, we also obtain the probabilities that the server is idle, busy, in working vacation, and in regular busy period, respectively. Finally, We introduce the application of the proposed model.

Keywords

Markov processes; discrete time systems; matrix algebra; probability; queueing theory; discrete time queueing system; embedded Markov chain; geometrical arrivals; matrix analysis solution method; negative customers; positive customers; probability generating function; regular busy period; single working vacation; stationary queue length; Analytical models; Computational modeling; Equations; Markov processes; Mathematical model; Queueing analysis; Servers; Discrete time queue; Negative customers; Single working vacation;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Research and Development (ICCRD), 2011 3rd International Conference on

Conference_Location

Shanghai

Print_ISBN

978-1-61284-839-6

Type

conf

DOI

10.1109/ICCRD.2011.5763843

Filename

5763843