MULTICLASS QUEUEING NETWORKS AND REFLECTING DIFFUSIONS

1/21/02


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Table of Contents

MULTICLASS QUEUEING NETWORKS AND REFLECTING DIFFUSIONS

QUEUEING NETWORKS

OUTLINE

Multiclass FIFO Station

Heavy Traffic Limit for Multiclass FIFO Station

Multiclass Queueing Network with Feedback

Multiclass Queuing Network: Model Equations

SRBM Approximations for Queueing Networks

SRBM Data

Deterministic Skorokhod Problem (SP)

Necessary Condition

Deterministic results

Stochastic Approach (SRBM)

Weak Existence and Uniqueness

Oscillation Inequality

Analysis of SRBMs

Positive Recurrence

Dai-Wang (93) Type Example (FIFO, multiclass + feedback)

Stability of Multiclass FIFO Networks

Multiclass Queuing Network: Model Equations

Heavy Traffic

A Sequence of Networks in Heavy Traffic

State Space Collapse

Reduced Form of Model Assuming MSSC

New Sufficient Conditions for a HT Limit Theorem

Dai-Wang-Wang example

RELATED RECENT WORK USING STATE SPACE COLLAPSE

Author: Williams