Geodesic
Optimal arrivals to a two-server loss system with random access
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 3, pp. 79-111

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We consider the 2-server queuing system with loss that admits requests during a time interval $[0,T]$. Players try to send their requests to the system, that provides a random access to its servers with some probabilities, and players know these probabilities. We consider a non-cooperative game for this queueing system. Each player's strategy is a time moment to send his request to the system trying to maximize the probability of successful service obtaining. We use a symmetric Nash equilibrium as an optimality criteria. Two models are considered for this game. In the first model the number of players is deterministic. In the second it follows a Poisson distribution. We prove that there exists a unique symmetric equilibrium for both models. Also we compare numerically equilibria for different models' parameters.
Keywords: queueing system, optimal arrivals, Nash equilibrium. 
@article{MGTA_2015_7_3_a3,
     author = {Julia V. Chirkova},
     title = {Optimal arrivals to a two-server loss system with random access},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {79--111},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2015_7_3_a3/}
}
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Julia V. Chirkova. Optimal arrivals to a two-server loss system with random access. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 3, pp. 79-111. http://geodesic.mathdoc.fr/item/MGTA_2015_7_3_a3/