Time-to-idle Control Variate Performance in the Single
Queue Case

  • Andrés Suárez-González ,
  • Cándido López-García,
  • José C. López-Ardao, 
  • Raúl Rodríguez Rubio, 
  • Miguel Rodríguez Pérez 
  • a,b,c,d,e atlanTTic research center, Universidade de Vigo, Escola de Enxeñaría de Telecomunicación, 36310 Vigo, Spain
Cite as
Suárez-González A., López-García C., López-Ardao J.C., Rodríguez Rubio R., Rodríguez Pérez M. (2021). Time-to-idle Control Variate Performance in the Single Queue Case. Proceedings of the 33rd European Modeling & Simulation Symposium (EMSS 2021), pp. 147-151. DOI: https://doi.org/10.46354/i3m.2021.emss.020


Control Variates (CV) is a Variance Reduction technique used in order to shorten simulation experiments. In a previous work we presented Time-to-idle as a stochastic process strongly correlated with the queue waiting time processes in the different queues of a polling service discipline network. Time-to-idle sample values are asynchronous with respect to those of queuing times, that is, they are generated at unpredictable times in an unpredictable order with respect to each other. This inherent characteristic allows it to be used in a network of queues (through batch means methods and taking care of synchronization between batches of both processes) but can hinge its performance in the single queue case. In this paper we evaluate its performance through simulation of the single queue case, comparing it with the service time and/or interarrival time synchronous random variables in the D/M/1, M/D/1 and M/M/1 queues where actual mean queue waiting times are known. We observe a slightly lower efficiency of Time-to-idle CV as was expected and we conclude that new techniques for synchronization of batches should be explored in order to minimize it.


  1. Adewunmi, A. and Aickelin, U. (2012). Investigating the effectiveness of variance reduction techniques in manufacturing, call center and cross-docking dis crete event simulation models. In Use Cases of Discrete Event Simulation, pages 1–26. Springer.  Guan, Z., Jia, Y., and He, M. (2019). A bidirectional 
  2. Guan, Z., Jia, Y., and He, M. (2019). A bidirectional polling MAC mechanism for IoT. Electronics, 8(6):715.
  3. Law, A. M. and Carson, J. S. (1979). A sequential procedure for determining the length of a steady-state simulation. Operations Research, 27(5):1011–1025.
  4. Loh, W. W. (1997). On the Method of Control Variates. PhD thesis, Stanford University.
  5. Ortiz-Gracia, L. (2020). Expected shortfall computation with multiple control variates. Applied Mathematics
    and Computation, 373:125018.
  6. Portier, F. and Segers, J. (2019). Monte carlo integration with a growing number of control variates. Journal of Applied Probability, 56(4):1168–1186.
  7. S. S. Lavenberg, T. L. M. and Welch, P. D. (1982). Sta- tistical results on control variables with application to queuing network simulation. Operations Research, 30:182–202.
  8. S. S. Lavengerg, T. L. M. and Sauer, C. H. (1979). Con comitant control variables applied to the regenerative simulation of queueing systems. Operations Research, 27:134–160. 
  9. Siddiqui, S., Ghani, S., and Khan, A. A. (2018). ADP MAC: An adaptive and dynamic polling-based MAC protocol for wireless sensor networks. IEEE Sensors Journal, 18(2):860–874. 
  10. Suárez-González, A., López-García, C., López-Ardao, J. C., and Fernández-Veiga, M. (2000). On the use of control variates in the simulation of medium access control protocols. In 2000 Winter Simulation Confer ence Proceedings (Cat. No. 00CH37165), volume 1, pages 782–787. IEEE. 
  11. Yang, Z.-J., Su, Y., Ding, H.-W., and Ding, Y.-Y. (2017). Strategies for improving the quality of polling service in wireless metropolitan area network. In MATEC Web of Conferences, volume 125, page 04019. EDP Sciences.
  12. Yang X.Y., Ripoll A., Marin I., Luque E. 2008. Genomic-scale analysis of DNA Words of Arbitrary Length by Parallel Computation. NIC Series, Vol. 33, 623–630.