Abstract
This paper considers a two-server random access system with loss that receives requests on a time interval [0, T]. The users (players) send their requests to the system, and then the system provides a random access to one of its two servers with some known probabilities. We study the following non-cooperative game for this service system. As his strategy, each player chooses the time to send his request to the system, trying to maximize the probability of servicing. The symmetric Nash equilibrium acts as the optimality criterion. Two models are considered for this game. In the first model the number of players is deterministic, while in the second it obeys the Poisson distribution. We demonstrate that there exists a unique symmetric equilibrium for both models. Finally, some numerical experiments are performed to compare the equilibria under different values of the model parameters.
Similar content being viewed by others
References
Mazalov, V.V. and Chuiko, Yu.V., Non-cooperative Nash Equilibrium in an Optimal Arrival Time Problem for Queuing System, Vychisl. Tekhnol., 2006, vol. 11, no. 6, pp. 60–71.
Roslyakov, A.V., Tsentry obsluzhivaniya vyzovov (Call Centres), Moscow: Eko-Trendz, 2002.
Altman, E., Applications of Dynamic Games in Queues, Adv. Dynamic Games, 2005, vol. 7, pp. 309–342.
Altman, E., A Markov Game Approach for Optimal Routing into a Queueing Network, INRIA report no. 2178, 1994.
Altman, E. and Hassin, R., Non-Threshold Equilibrium for Customers Joining an M/G/1 Queue, Proc. of 10th Int. Symp. on Dynamic Game and Applications, 2002.
Altman, E., Jimenez, T., Nunez Queija, R. and Yechiali, U., Optimal Routing among ·/M/1 Queues with Partial Information, Stoch. Models, 2004, vol. 20, no. 2, pp. 149–172.
Altman, E. and Koole, G., Stochastic Scheduling Games with Markov Decision Arrival Processes, J. Comput. Math. Appl., 1993, vol. 26, no. 6, pp. 141–148.
Altman, E. and Shimkin, N., Individually Optimal Dynamic Routing in a Processor Sharing System, Operat. Res., 1998, pp. 776–784.
Glazer, A. and Hassin, R., Equilibrium Arrivals in Queues with Bulk Service at Scheduled Times, Transport. Sci., 1987, vol. 21, no. 4, pp. 273–278.
Glazer, A. and Hassin, R., ?/M/1: On the Equilibrium Distribution of Customer Arrivals, Eur. J. Operat. Res., 1983, vol. 13, no. 2, pp. 146–150.
Killelea, P., Web Performance Tuning: Speeding Up the Web, Sebastopol: O’Reilly Media, 2002.
Kopper, K., The Linux Enterprise Cluster: Build a Highly Available Cluster with Commodity Hardware and Free Software, San Francisco: No Starch Press, 2005.
Ou, Z., Zhuang, H., Lukyanenko, A., Nurminen, J., Hui, P., Mazalov, V., and Yla-Jaaski, A., Is the Same Instance Type Created Equal? Exploiting Heterogeneity of Public Clouds, IEEE Trans. Cloud Computing, 2013, DOI: 10.1109/TCC.2013.12.
Ravner, L. and Haviv, M., Strategic Timing of Arrivals to a Finite Queue Multi-Server Loss System, Queueing Syst., 2015, vol. 81, no. 1, pp. 71–96.
Ravner, L. and Haviv, M., Equilibrium and Socially Optimal Arrivals to a Single Server Loss System, in Int. Conf. on Network Games Control and Optimization 2014 (NETGCOOP’14), Trento, Italy, October 2014.
Shaked, M. and Shanthikumar, J.G., Stochastic Orders, Springer Series in Statistics, New York: Springer, 2007.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © Yu.V. Chirkova, 2015, published in Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2015, No. 3, pp. 79–111.
Rights and permissions
About this article
Cite this article
Chirkova, Y.V. Optimal arrivals in a two-server random access system with loss. Autom Remote Control 78, 557–580 (2017). https://doi.org/10.1134/S0005117917030146
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117917030146