Geodesic
Pricing in queueing systems $M/M/m$ with delays
Contributions to game theory and management, Tome 7 (2014), pp. 214-220.

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A non-cooperative $m$-person game which is related to the queueing system $ M/M/m $ is considered. There are n competing transport companies which serve the stream of customers with exponential distribution with parameters $\mu_i$, $i=1, 2,...,m$ respectively. The stream forms the Poisson process with intensity $\lambda$. The problem of pricing and determining the optimal intensity for each player in the competition is solved.
Keywords: Duopoly, equilibrium prices, queueing system. 
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Anna V. Melnik. Pricing in queueing systems $M/M/m$ with delays. Contributions to game theory and management, Tome 7 (2014), pp. 214-220. http://geodesic.mathdoc.fr/item/CGTM_2014_7_a18/

[1] Hotelling H., “Stability in Competition”, Economic Journal, 39 (1929), 41–57

[2] D'Aspremont C., Gabszewicz J., Thisse J.-F., “On Hotelling's “Stability in Competition””, Econometrica, 47 (1979), 1145–1150 | DOI | MR | Zbl

[3] Mazalova A. V., “Hotelling's duopoly on the plane with Manhattan distance”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2012, no. 2, 33–43 (in Russian)

[4] Altman E., Shimkin N., “Individual equilibrium and learning in processor sharing systems”, Operations Research, 46 (1998), 776–784 | DOI | Zbl

[5] Levhari D., Luski I., “Duopoly pricing and waiting lines”, European Economic Review, 11 (1978), 17–35 | DOI

[6] Hassin R., Haviv M., To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems, Springer, 2003 | MR

[7] Luski I., “On partial equilibrium in a queueing system with two services”, The Review of Economic Studies, 43 (1976), 519–525 | DOI | Zbl

[8] Koryagin M. E., “Competition of public transport flows”, Autom. Remote Control, 69:8 (1986), 1380–1389 | DOI | MR

[9] Taha H. A., Operations Research: An Introduction, 9th. edition, Prentice Hall, 2011 | MR | Zbl

[10] Mazalova A. V., “Duopoly in queueing system”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2013, no. 4, 32–41 (in Russian)