The Annals of Applied Probability

Heavy Traffic Limits for Some Queueing Networks

Maury Bramson and J.G. Dai

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Using a slight modification of the framework of Bramson [7] and Williams [54], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single-station systems operating under first-in-first-out (FIFO), generalized-head-of-the-line proportional processor sharing (GHLPPS) and static buffer priority (SBP) service disciplines. The next two families are reentrant lines that operate under first-buffer-first-serve (FBFS) and last-buffer-first-serve (LBFS) service disciplines; the last family consists of certain two-station, five-class networks operating under an SBP service discipline. Some of these heavy traffic limits have appeared earlier in the literature; our new proofs demonstrate the significant simplifications that can be achieved in the present setting.

Article information

Ann. Appl. Probab., Volume 11, Number 1 (2001), 49-90.

First available in Project Euclid: 27 August 2001

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60F17: Functional limit theorems; invariance principles 60G17: Sample path properties
Secondary: 60J15 90B22: Queues and service [See also 60K25, 68M20] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]

multiclass queueing network Brownian model heavy traffic reflecting Brownian motion diffusion approximation


Bramson, Maury; Dai, J.G. Heavy Traffic Limits for Some Queueing Networks. Ann. Appl. Probab. 11 (2001), no. 1, 49--90. doi:10.1214/aoap/998926987.

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