QUEUEING THEORY / INTERACTIVE LAB
Queueing & Staffing Lab.
Translate stochastic demand and service capacity into utilization, waiting and response-time staffing.
ANALYTICAL QUEUEING
M/M/c · NO ABANDONMENTErlang C × Little’s Law
UTILIZATION ρ67%
P(WAIT)28%
AVG WAIT Wq2.8m
SERVICE LEVEL93.6%
WIP / L4.6
90% ≤ 15m6 staff
STAFFING RESPONSE · SERVICE LEVEL + AVG WAIT
● SERVICE LEVEL– AVG WAIT (scaled)CURRENT c=6 · REQUIRED c=6
ERLANG C ANSWERS
How much capacity is needed to hit a response-time target?
Using λ=12/hr, mean service=20 min and c=6, Erlang C estimates waiting probability and the distribution of queue delay.
P(W>t) = C(c,a) · e^−(cμ−λ)tLITTLE'S LAW ANSWERS
How are average inventory, throughput and time related?
At steady state, the same model implies L = λW and Lq = λWq. Little’s Law is an identity; it does not determine the staffing level by itself.
L = λW = 4.57Illustrative inspection-callboard analogy: mechanics generate inspection requests, QA personnel are parallel servers, and the service-level goal is 90% answered within the selected response target. Erlang C assumes Poisson arrivals, exponential service, one pooled queue, independent identical servers, infinite waiting capacity and no abandonment.