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2017 | OriginalPaper | Buchkapitel

Stability Analysis of a Basic Collaboration System via Fluid Limits

verfasst von : Rosario Delgado, Evsey Morozov

Erschienen in: Computer Networks

Verlag: Springer International Publishing

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Abstract

In this work, the fluid limit approach methodology is applied to find a sufficient and necessary stability condition for the Basic Collaboration (BC) system with feedback allowed, which is a generalization of the so-called W-model. In this queueing system, some customer classes need cooperation of a subset of (non-overlapping) servers. We assume that each customer class arrives to the system following a renewal input with general i.i.d. inter-arrival times, and general i.i.d. service times are also assumed. Priority is given to customer classes that can not be served by a single server but need a cooperation.

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Literatur
1.
Zurück zum Zitat Arthurs, E., Kaufman, J.S.: Sizing a message store subject to blocking criteria. In: Proceedings of the Third International Symposium on Modelling and Performance Evaluation of Computer Systems: Performance of Computer Systems, pp. 547–564. North-Holland Publishing Co., Amsterdam (1979) Arthurs, E., Kaufman, J.S.: Sizing a message store subject to blocking criteria. In: Proceedings of the Third International Symposium on Modelling and Performance Evaluation of Computer Systems: Performance of Computer Systems, pp. 547–564. North-Holland Publishing Co., Amsterdam (1979)
2.
Zurück zum Zitat Brill, P., Green, L.: Queues in which customers receive simultaneous service from a random number of servers: a system point approach. Manage. Sci. 30(1), 51–68 (1984)MathSciNetCrossRefMATH Brill, P., Green, L.: Queues in which customers receive simultaneous service from a random number of servers: a system point approach. Manage. Sci. 30(1), 51–68 (1984)MathSciNetCrossRefMATH
3.
Zurück zum Zitat Dai, J.G.: On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models. Ann. Appl. Prob. 5(1), 49–77 (1995)MathSciNetCrossRefMATH Dai, J.G.: On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models. Ann. Appl. Prob. 5(1), 49–77 (1995)MathSciNetCrossRefMATH
4.
Zurück zum Zitat Dai, J.G.: A fluid limit model criterion for unstability of multiclass queueing networks. Ann. Appl. Prob. 6(3), 751–757 (1996)MathSciNetCrossRefMATH Dai, J.G.: A fluid limit model criterion for unstability of multiclass queueing networks. Ann. Appl. Prob. 6(3), 751–757 (1996)MathSciNetCrossRefMATH
5.
Zurück zum Zitat Davis, M.H.A.: Piecewise deterministic Markov processes: a general class of non-diffusion stochastic models. J. Roy. Statist. Soc. Ser. B. 46, 353–388 (1984)MathSciNetMATH Davis, M.H.A.: Piecewise deterministic Markov processes: a general class of non-diffusion stochastic models. J. Roy. Statist. Soc. Ser. B. 46, 353–388 (1984)MathSciNetMATH
7.
Zurück zum Zitat Delgado, R., Morozov, E.: Stability analysis of cascade networks via fluid models. Perform. Eval. 82, 39–54 (2014)CrossRef Delgado, R., Morozov, E.: Stability analysis of cascade networks via fluid models. Perform. Eval. 82, 39–54 (2014)CrossRef
8.
Zurück zum Zitat Fletcher, G.Y., Perros, H., Stewart, W.: A queueing system where customers require a random number of servers simultaneously. Eur. J. Oper. Res. 23, 331–342 (1986)MathSciNetCrossRefMATH Fletcher, G.Y., Perros, H., Stewart, W.: A queueing system where customers require a random number of servers simultaneously. Eur. J. Oper. Res. 23, 331–342 (1986)MathSciNetCrossRefMATH
10.
Zurück zum Zitat Green, L.: Comparing operating characteristics of queues in which customers require a random number of servers. Manage. Sci. 27(1), 65–74 (1980)MathSciNetCrossRefMATH Green, L.: Comparing operating characteristics of queues in which customers require a random number of servers. Manage. Sci. 27(1), 65–74 (1980)MathSciNetCrossRefMATH
11.
Zurück zum Zitat Kaufman, J.: Blocking in a shared resource environment. IEEE Trans. Commun. 29(10), 1474–1481 (1981)CrossRef Kaufman, J.: Blocking in a shared resource environment. IEEE Trans. Commun. 29(10), 1474–1481 (1981)CrossRef
13.
Zurück zum Zitat Kim, S.: M/M/s queueing system where customers demand multiple server use. Ph.D. thesis, Southern Methodist University (1979) Kim, S.: M/M/s queueing system where customers demand multiple server use. Ph.D. thesis, Southern Methodist University (1979)
15.
Zurück zum Zitat Talreja, R., Whitt, W.: Fluid models for overloaded multiclass many-server queueing systems with first-come, first-served routing. Manage. Sci. 54, 1513–1527 (2008)CrossRefMATH Talreja, R., Whitt, W.: Fluid models for overloaded multiclass many-server queueing systems with first-come, first-served routing. Manage. Sci. 54, 1513–1527 (2008)CrossRefMATH
16.
Zurück zum Zitat Tikhonenko, O.: Generalized erlang problem for service systems with finite total capacity. Probl. Inf. Transm. 41(3), 243–253 (2005)MathSciNetCrossRefMATH Tikhonenko, O.: Generalized erlang problem for service systems with finite total capacity. Probl. Inf. Transm. 41(3), 243–253 (2005)MathSciNetCrossRefMATH
17.
Zurück zum Zitat Van Dijk, N.M.: Blocking of finite source inputs which require simultaneous servers with general think and holding times. Oper. Res. Lett. 8(1), 45–52 (1989)MathSciNetCrossRefMATH Van Dijk, N.M.: Blocking of finite source inputs which require simultaneous servers with general think and holding times. Oper. Res. Lett. 8(1), 45–52 (1989)MathSciNetCrossRefMATH
18.
19.
Zurück zum Zitat Wong, D., Paciorek, N., Walsh, T., DiCelie, J., Young, M., Peet, B.: Concordia: an infrastructure for collaborating mobile agents. In: Rothermel, K., Popescu-Zeletin, R. (eds.) MA 1997. LNCS, vol. 1219, pp. 86–97. Springer, Heidelberg (1997). doi:10.1007/3-540-62803-7_26 CrossRef Wong, D., Paciorek, N., Walsh, T., DiCelie, J., Young, M., Peet, B.: Concordia: an infrastructure for collaborating mobile agents. In: Rothermel, K., Popescu-Zeletin, R. (eds.) MA 1997. LNCS, vol. 1219, pp. 86–97. Springer, Heidelberg (1997). doi:10.​1007/​3-540-62803-7_​26 CrossRef
Metadaten
Titel
Stability Analysis of a Basic Collaboration System via Fluid Limits
verfasst von
Rosario Delgado
Evsey Morozov
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-59767-6_28

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