Towards a Stochastic Network Calculus Jorg Liebeherr University

Towards a Stochastic Network Calculus Jorg Liebeherr University of Toronto

Delay Guarantees Sender Switch Receiver • A deterministic service gives worst-case guarantees Delay d • A statistical service provides probabilistic guarantees Pr[ Delay d ]

Multiplexing Gain Sources of multiplexing gain: • Traffic Conditioning (“Smoothing”) • Scheduling • Statistical Multiplexing Gain

Why is it hard to get multiplexing gain? 1. Burstiness of traffic 2. Stringent service guarantees Peak rate Mean rate

Traffic Shaping Traffic Conditioning • Traffic shaping is typically done at the network edge

Scheduling • Scheduling algorithm determines the order in which traffic is transmitted

Expected case Deterministic worst-case Probable worstcase

Designing Networks for Multiplexing Gain Scheduling Earliest-Deadline-First GPS Static Priority FCFS Peak Rate Allocation Deterministic service Statistical service Average Rate Service / Admission Control Peak Rate Token Bucket Multiple Buckets Traffic Characterization/ Conditioning

Designing Networks for Multiplexing Gain Scheduling Earliest-Deadline-First GPS Static Priority FCFS Peak Rate Allocation Deterministic service Statistical service Average Rate Service / Admission Control Peak Rate Token Bucket Multiple Buckets Traffic Characterization/ Conditioning

Designing Networks for Multiplexing Gain Scheduling Earliest-Deadline-First By now: The design space for deterministic guarantees is well understood. GPS Static Priority FCFS Peak Rate Allocation Deterministic service Statistical service Average Rate Service / Admission Control Peak Rate Token Bucket Multiple Buckets Traffic Characterization/ Conditioning

Designing Networks for Multiplexing Gain Scheduling Earliest-Deadline-First GPS Static Priority FCFS Peak Rate Allocation Deterministic service Statistical service Average Rate Service / Admission Control Peak Rate Token Bucket Multiple Buckets Traffic Characterization/ Conditioning