Abstract
A c–server queueing system providing service to two types of customers, say, Type 1 and Type 2 to which customers arrive according to a marked Poisson process is considered. A Type 1 customer has to receive service by one of c servers while a Type 2 customer may be served by a Type 1 customer (with probability p) who is available to act as a server soon after getting own service or by one of c servers. Upon completion of a service a free server will offer service to a Type 1 customer on a FCFS basis. However, if there is no Type 1 customer waiting in the system, that server will serve a Type 2 customer if one of that type is present in the queue. The service time is exponentially distributed for each category. We consider preemptive service discipline. Condition for system stability is established. Crucial system characteristics are computed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Brodal, G.S.: A survey on priority queues. In: Brodnik, A., López-Ortiz, A., Raman, V., Viola, A. (eds.) Space-Efficient Data Structures, Streams, and Algorithms. LNCS, vol. 8066, pp. 150–163. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40273-9_11
Chakravarthy, S.R., Dudin, A.N.: A queueing model for crowdsourcing. J. Oper. Res. Soc. 68, 221–236 (2016)
Howe, J.: Crowdsourcing: a definition (2006). http://www.crowdsourcing.com/cs/2006/06/crowdsourcing_a.html
Jaiswal, N.K.: Preemptive resume priority queue. Oper. Res. 9, 732–742 (1961)
Jaiswal, N.K.: Priority Queues. Academic Press, New York, London (1968)
Krishnamoorthy, A., Pramod, P.K., Chakravarthy, S.R.: Queues with interruptions, a survey. Top 22(1), 290–320 (2014)
Latouche, G., Ramaswami, V.: An Introduction to Matrix Analytic Methods in Stochastic Modeling. SIAM, Philadelphia (1999)
Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press, Baltimore (1981). [1994 version is Dover Edition]
Takagi, H.: Queueing Analysis: Vacations and Priority Systems, vol. 1. North-Holland, Amsterdam (1991)
Acknowledgments
Research of the first and second authors is supported by Kerala State Council for Science, Technology & Environment (No. 001/KESS/2013/CSTE). Research of the third author is supported by the University Grants Commission, Government of India, under Faculty Development Programme (Grant No. F. FIP/12th Plan/KLMG003TF05).
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., Shajin, D., Manjunath, A.S. (2017). On a Multi-server Priority Queue with Preemption in Crowdsourcing. In: Rykov, V., Singpurwalla, N., Zubkov, A. (eds) Analytical and Computational Methods in Probability Theory. ACMPT 2017. Lecture Notes in Computer Science(), vol 10684. Springer, Cham. https://doi.org/10.1007/978-3-319-71504-9_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-71504-9_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-71503-2
Online ISBN: 978-3-319-71504-9
eBook Packages: Computer ScienceComputer Science (R0)