Abstract
We consider a single server queueing model with two parallel queues in which one is finite buffer and the other is infinite. Customers arrive according to two independent Poisson processes and service time follows phase type distribution. Customers receive service on the basis of a token system. Customers in the infinite queue are ordinary customers and the customers in the finite queue are priority customers. Customer priority may be either by paying a cost or by any other means. Priority customers have the right to make the strategic decision regarding the queue to which he or she may join. Priority customers are provided service on the basis of token issued to such customers to access the service according to the rule: when \( N-1 \) customers of lower priority are consecutively served, the next to be served is from the priority line, if there is one waiting, thus ensuring there reduced waiting time. However they can join the lower priority queue in the case they find the waiting time less. This strategy will be discussed in the paper. We perform the steady state analysis and establish the stability condition of the queueing model. Some performance measures are also evaluated. Control problem has been discussed. Some numerical illustrations are provided.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Artalejo, J.R., Gomez-Corral, A.: On a single server queue with negative arrivals and request repeated. J. Appl. Probab. 36, 907–918 (1999)
Chakravarthy, S.: A finite capacity dynamic priority queueing model. Comput. Ind. Eng. 22, 369–385 (1992)
Chakravarthy, S., Thiagarajan, S.: Two parallel queues with simultaneous services and Markovian arrivals. J. Appl. Math. Stoch. Anal. 10, 383–405 (1997)
Green, L.: Queueing analysis in healthcare. Patient flow reducing delay in healthcare delivery (2006). Edited by Randolph Hall
Jaiswal, N.K.: Priority Queues. Academic press, New York (1968)
Keams, P., Peterson, S.: Performance analysis of a token based distributed mutual exclusion protocol. In: Proceedings Southeast Conference (1993)
Krishnamoorthy, A., Deepak, T.G., Joshua, V.C.: Queues with postponed work. Top 12, 375–398 (2004)
Latouche, G., Ramaswami, V.: Introduction to Matrix Analytic Methods in Stochastic Modelling. SIAM (1999)
Lyan Mark, A., Peha Jon, M.: The priority token bank in a network of queues. In: Proceedings ICC (1997)
Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models - An Algorithmic Approach. The Johns Hopkins University Press, Baltimore (1981)
Neuts, M.F.: Markov chains with applications in queueing theory which have a matrix-geometric invariant probability vector. Adv. Appl. Probab. 10, 185–212 (1978)
Neuts, M.F., He, Q.-M.: Two M/M/1 queue with transfer of customers. Queueing Syst. 42, 377–400 (2002)
Patil, R.R.: Token based fair queueing algorithms for wireless networks. IJSEAT 2, 121–124 (2014)
Peha, J.M.: The priority token: integrated scheduling and admission control for an integrated services network. In: ICC(1993)
Sharma, V., Virtamo, J.T.: A finite buffer queue with priority. Perform. Eval. 47, 1–22 (2002)
Acknowledgement
The work of the third author is supported by the Maulana Azad National fellowship \([F1-17.1/2015-16/MANF-2015-17-KER-65493]\) of University Grants commission, India.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Krishnamoorthy, A., Joshua, V.C., Babu, D. (2017). A Token Based Parallel Processing Queueing System with Priority. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2017. Communications in Computer and Information Science, vol 700. Springer, Cham. https://doi.org/10.1007/978-3-319-66836-9_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-66836-9_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66835-2
Online ISBN: 978-3-319-66836-9
eBook Packages: Computer ScienceComputer Science (R0)