Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T21:08:17.779Z Has data issue: false hasContentIssue false
  • English
  • Français

IMPROVING THE PERFORMANCE OF POLLING MODELS USING FORCED IDLE TIMES

Published online by Cambridge University Press:  20 November 2017

Frank Aurzada  and
Sebastian Schwinn
Frank Aurzada
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany E-mail: [email protected]
Sebastian Schwinn
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany Graduate School CE, Technische Universität Darmstadt, Darmstadt, Germany E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider polling models in the sense of Takagi [19]. In our case, the feature of the server is that it may be forced to wait idly for new messages at an empty queue instead of switching to the next station. We propose four different wait-and-see strategies that govern these waiting periods. We assume Poisson arrivals for new messages and allow general service and switchover time distributions. The results are formulas for the mean average queueing delay and characterizations of the cases where the wait-and-see strategies yield a lower delay compared with the exhaustive strategy.

Keywords

exhaustive serviceforced idle timepatient serverpolling modelpseudo-conservation lawtimerwait-and-see strategywaiting time
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 4 , October 2018 , pp. 580 - 602
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Afanassieva, L.G., Delcoigne, F., & Fayolle, G. (1997). On polling systems where servers wait for customers. Markov Processes and Related Fields 3(4): 527–545.Google Scholar
2.Al Hanbali, A., de Haan, R., Boucherie, R.J., & van Ommeren, J.-K. (2012). Time-limited polling systems with batch arrivals and phase-type service times. Annals of Operations Research 198(1): 57–82.Google Scholar
3.Asmussen, S. (1987). Applied probability and queues. Wiley series in probability and mathematical statistics. Chichester: Wiley.Google Scholar
4.Aurzada, F., Beck, S., & Scheutzow, M. (2012). Wait-and-see strategies in polling models. Probability in the Engineering and Informational Sciences 26(1): 17–42.Google Scholar
5.Boxma, O.J. & Groenendijk, W.P. (1987). Pseudo-conservation laws in cyclic-service systems. Journal of Applied Probability 24(4): 949–964.Google Scholar
6.Boxma, O.J., Schlegel, S., & Yechiali, U. (2002). Two-queue polling models with a patient server. Annals of Operations Research 112(1): 101–121.Google Scholar
7.Cooper, R.B., Niu, S.-C., & Srinivasan, M.M. (1998). When does forced idle time improve performance in polling models? Management Science 44(8): 1079–1086.Google Scholar
8.de Haan, R. (2009). Queueing models for mobile ad hoc networks. Ph.D. thesis, University of Twente, Enschede.Google Scholar
9.de Haan, R., Boucherie, R.J., & van Ommeren, J.-K. (2009). A polling model with an autonomous server. Queueing Systems 62(3): 279–308.Google Scholar
10.de Souza e Silva, E., Gail, H.R., & Muntz, R.R. (1995). Polling systems with server timeouts and their application to token passing networks. IEEE/ACM Transactions on Networking 3(5): 560–575.Google Scholar
11.Eliazar, I. & Yechiali, U. (1998). Polling under the randomly timed gated regime. Communications in Statistics. Stochastic Models 14(1–2): 79–93.Google Scholar
12.Frigui, I. & Alfa, A.-S. (1998). Analysis of a time-limited polling system. Computer Communications 21(6): 558–571.Google Scholar
13.Kleinrock, L. (1975). Queueing systems, Volume I: Theory. New York: Wiley.Google Scholar
14.Leung, K.K. (1994). Cyclic-service systems with nonpreemptive, time-limited service. IEEE Transactions on Communications 42(8): 2521–2524.Google Scholar
15.Li, J.Z. (2009). Two-queue polling model with a timer and a randomly-timed gated mechanism. Journal of Mathematical Research and Exposition 29(4): 721–729.Google Scholar
16.Peköz, E.A. (1999). More on using forced idle time to improve performance in polling models. Probability in the Engineering and Informational Sciences 13(4): 489–496.Google Scholar
17.Samaddar, S. & Whalen, T. (2008). Improving performance in cyclic production systems by using forced variable idle setup time. Manufacturing & Service Operations Management 10(2): 173–180.Google Scholar
18.Sarkar, D. & Zangwill, W.I. (1991). Variance effects in cyclic production systems. Management Science 37(4): 444–453.Google Scholar
19.Takagi, H. (1986). Analysis of polling systems. Cambridge: The MIT Press.Google Scholar
20.Xie, J., Fischer, M.J., & Harris, C.M. (1997). Workload and waiting time in a fixed-time loop system. Computers & Operations Research 24(8): 789–803.Google Scholar