Abstract. This paper continues the development of policy synthesis techniques for large processing networks based upon a linear
uid model. It is shown that (i) A relaxation of the
uid model based on workload leads to an optimization problem of lower dimension. The relaxed control problem admits a pathwise optimal solution in many instances. (ii) A translation to the original
uid model is almost optimal, with vanishing relative error as the network load approaches one. It is pathwise optimal after a short transient period, provided a pathwise optimal solution exists for the relaxed control problem. (iii) A similar translation to the stochastic network model is almost pathwise optimal in heavy trac, again with vanishing relative error. The regret is of order j log(1 )j.
|
1681
|
Random Early Detection Gateways for Congestion Avoidance
– Floyd, Jacobson
- 1993
|
|
510
|
A Calculus for Network Delay, Part I: Network Elements in Isolation
– Cruz
- 1991
|
|
139
|
On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models
– Dai
- 1995
|
|
107
|
Computer Performance Modeling Handbook
– Lavenberg, editor
- 1983
|
|
84
|
Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems
– Kumar, Seidman
- 1990
|
|
81
|
Applying a new device in the optimization of exponential queuing systems
– Lippman
- 1975
|
|
74
|
On the ergodicity of stochastic processes describing open queueing networks, Problemi Peredachi Informatsii 28
– Rybko, Stolyar
- 1992
|
|
69
|
Instability of FIFO queueing networks
– Bramson
- 1994
|
|
62
|
Manufacturing system engineering
– Gershwin
- 1994
|
|
57
|
Stability and convergence of moments for multiclass queueing networks via fluid limit models
– DAI, MEYN
- 1995
|
|
56
|
Performance bounds for queueing networks and scheduling policies
– Kumar, Kumar
- 1994
|
|
53
|
Scheduling networks of queues: Heavy traffic analysis of a two-station network with controllable input
– Wein
|
|
44
|
Optimization of multiclass queueing networks: Polyhedral and nonlinear characterizations of achievable performance
– Paschaladis, Tsitsiklis
- 1994
|
|
44
|
Large Deviations for Performance Analysis: Queues, Communication and Computing
– Shwartz, Weiss
- 1995
|
|
43
|
Discrete flow networks: Bottleneck analysis and fluid
– Chen, Mandelbaum
- 1991
|
|
43
|
Optimal control of two interacting service stations
– Hajek
- 1984
|
|
43
|
State space collapse with applications to heavytraffic limits for multiclass queueing networks
– Bramson
- 1998
|
|
42
|
Duality and linear programs for stability and performance analysis of queueing networks and scheduling policies
– Kumar, Meyn
- 1996
|
|
39
|
Performance Bounds for Flow Control Protocols
– Agrawal, Cruz, et al.
|
|
37
|
2001. Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: Asymptotic optimality of a threshold policy
– Bell, Williams
|
|
37
|
Transience of multiclass queueing networks and their fluid models
– Meyn
- 1995
|
|
35
|
Planning queueing simulations
– Whitt
- 1989
|
|
34
|
Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling,” Queueing Systems
– Kelly, Laws
- 1993
|
|
30
|
Stability of generalized Jackson networks
– Meyn, Down
- 1994
|
|
29
|
Stability and instability of fluid models for re-entrant lines
– Dai, Weiss
- 1996
|
|
27
|
Lyapunov functions for semimartingale reflecting Brownian motions
– Dupuis, Williams
- 1994
|
|
26
|
A fluid-limit model criterion for instability of multiclass queueing networks
– Dai
- 1996
|
|
25
|
Brownian Models of Open Processing Networks: Canonical Representation of Workload
– Harrison
|
|
24
|
Optimal control of a queueing system with two heterogeneous servers
– Lin, PR
- 1984
|
|
23
|
Fluctuation smoothing policies are stable for stochastic reentrant lines. Discrete Event Dynamical Systems
– Kumar, Kumar
- 1996
|
|
22
|
Convex duality and the Skorokhod Problem
– Dupuis, Ramanan
- 1999
|
|
21
|
Dynamic scheduling of multiclass fluid networks
– Chen, Yao
- 1993
|
|
20
|
Heavy Traffic Resource Pooling in Parallel-Server Systems
– Harrison, Lopez
- 1999
|
|
18
|
The BIGSTEP approach to flow management in stochastic processing networks
– Harrison
- 1996
|
|
17
|
Value iteration and optimization of multiclass queueing networks, Queueing Systems Theory and Applications
– Chen, Meyn
- 1999
|
|
17
|
Scheduling semiconductor lines using a fluid network model
– Connors, Feigin, et al.
- 1994
|
|
15
|
Fluid network models: Linear programs for control and performance bounds
– Eng, Humphrey, et al.
- 1996
|
|
14
|
The policy improvement algorithm for Markov decision processes
– Meyn
- 1997
|
|
13
|
Queueing simulation in heavy traffic
– Asmussen
- 1992
|
|
13
|
Spectral theory and limit theorems for geometrically ergodic Markov processes
– Kontoyiannis, Meyn
- 2001
|
|
11
|
The delay of open markovian queueing networks: Uniform functional bounds, heavy trac pole multiplicities, and stability
– Humes, Ou, et al.
- 1997
|
|
11
|
A new algorithm for state-constrained separated continuous linear programming
– Luo, Bertsimas
- 1998
|
|
10
|
Stochastic monotonicity in general queueing networks
– Shanthikumar, Yao
- 1989
|
|
9
|
Performance bounds for scheduling queueing networks
– Ou, Wein
- 1992
|
|
7
|
A fluid heuristic for minimizing makespan in job shops
– Dai, Weiss
- 2002
|
|
7
|
Stability and optimization of multiclass queueing networks and their fluid models
– Meyn
- 1997
|
|
6
|
A Multiclass Feedback Queueing Network with a Regular Skorokhod Problem
– Dupuis, Ramanan
- 1999
|
|
6
|
Variance reduction for simulation in multiclass queueing networks
– Henderson, Meyn
- 1999
|
|
5
|
Asymptotic optimality of tracking-policies in stochastic networks
– Baeuerle
- 2000
|
|
5
|
Brownian models of heterogeneous customer populations
– Harrison
- 1988
|
|
