II. QUEUING THEORY (a) General Concepts - queuing theory useful ...
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II. QUEUING THEORY (a) General Concepts - queuing theory useful ...
queuing theory useful for considering performance ... (in theory), # queued
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II. QUEUING THEORY
(a) General Concepts - queuing theory useful for considering performance analysis of packet switching and circuit switching General model of a queue:
- in practice, queue size is finite (i.e., number of packets that can be queued is limited → extra packets discarded → "blocking") - if λ > μ ⇒ # queued packets will grow until queue saturated (remains full) or if queue size allowed to be ∞ (in theory), # queued packets will grow without bound - ρ = λ/μ = utilization or traffic intensity
QUEUING
1
- as ρ → 1, queue becomes unstable - factors of interest: time delay, blocking performance, packet throughput (packets/time to get through) - queue modelled by considering (1) packet arrival statistics (2) service time distribution (i.e., packet length distribution) (3) service discipline - FIFO, priority discipline (4) buffer size (5) input population (finite or ∞) (b) Poisson Process - arrival process (eg. packets generated at input to packet switch network or call initiated in circuit switch network) are often assumed to be Poisson - continuous time:
- discrete time:
QUEUING
2
- divide time t into n intervals of length Δt (very small) - let probability of arrival to queue in interval Δt = p+ and assume all arrival events are independent (i.e., memoryless) - assume Δt is small enough so that probability of ≥ 2 arrivals in Δt is negligible, i.e., p+
