Abstract
We present two multiclass queueing networks where the Brownian models proposed by Harrison and Nguyen [3,4] do not exist. If self-feedback is allowed, we can construct such an example with a two-station network. For a three-station network, we can construct such an example without self-feedback.
Similar content being viewed by others
References
J.G. Dai, V. Nguyen and M.I. Reiman, Sequential bottleneck decomposition: An approximation method for open queueing networks, Oper. Res., to appear.
J.M. Harrison, Brownian models of queueing networks with heterogeneous customer populations,Proc. IMA Workshop on Stochastic Differential Systems (Springer, 1988).
J.M. Harrison and V. Nguyen, The QNET method for two-moment analysis of open queueing networks, Queueing Systems 6 (1990) 1–32.
J.M. Harrison and V. Nguyen, Brownian models of multiclass queueing networks: Current status and open problems, Queueing Systems 13 (1993), this issue.
J.M. Harrison and M.I. Reiman, Reflected Brownian motion on an orthant, Ann. Prob. 9 (1981) 302–308.
J.G. Dai and T.G. Kurtz, A multiclass station with Markovian feedback in heavy traffic, Preprint.
W.P. Peterson, A heavy traffic limit theorem for networks of queues with multiple customer types, Math. Oper. Res. 16 (1991) 90–118.
M.I. Reiman, Open queueing networks in heavy traffic, Math. Oper. Res. 9 (1984) 441–458.
M.I. Reiman, A multiclass feedback queue in heavy traffic, Adv. Appl. Prob. 20 (1988) 179–207.
M.I. Reiman and R.J. Williams, A boundary property of semimartingale reflecting Brownian motions, Prob. Theory Rel. Fields 77 (1988) 87–97 and 80 (1989) 633.
L.M. Taylor and R.J. Williams, Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant, Prob. Theory Rel. Fields, to appear.
Author information
Authors and Affiliations
Additional information
Research supported in part by Texas Instruments Corporation Grant 90456-034.
Rights and permissions
About this article
Cite this article
Dai, J.G., Wang, Y. Nonexistence of Brownian models for certain multiclass queueing networks. Queueing Syst 13, 41–46 (1993). https://doi.org/10.1007/BF01158928
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01158928