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
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