Queuing-Calculator

The formulas in this Python script implement the simple queueing models described in Chapter 6 of Banks, Carson, Nelson and Nicol, Discrete-Event System Simulation, 5th edition.

This project was a conversion of a macro-enabled VBA document created by Professor Barry Nelson.

Supported Queues:

• M/G/1
• M/M/c
• M/G/c
• M/M/c/N
• M/M/c/K/K

Input Parameter Definitions:

• lmda: "λ" i.e. arrival rate
• mu: "μ" i.e. service rate
• c: number of servers
• sigma2: "σ²" i.e. variance of service time
• n: system capacity, including customers in service
• k: size of calling population

Output Parameter Definitions:

• rho: "ρ" i.e. utilization
• l: mean number in system
• w: mean time in system
• wq: mean time in queue
• lq: mean number in queue
• p0: probability of empty system
• lmda_effective: "λ_effective" i.e. effective arrival rate

Usage Examples:

After import queueing as q:

• rho, l, w, wq, lq, p0 = q.eval_MG1(lmda=1.125, mu=2.35, sigma2=0.2)
• rho, l, w, wq, lq, p0 = q.eval_MMc(lmda=3.6, mu=2.15, c=3)
• rho, l, w, wq, lq = q.eval_MGc(lmda=5.42, mu=2.18, c=3, sigma2=0.56)
• rho, l, w, wq, lq, p0, pN, lmda_effective = q.eval_MMcN(lmda=12.98, mu=3.47, c=4, n=15)
• rho, l, w, wq, lq, p0, lmda_effective = q.eval_MMcK(lmda=2.65, mu=1.2, c=5, k=6)