◇ Math reference · Part 01
Kendall notation
The standard six-slot taxonomy for naming queueing systems — and the namesake of this product.
Every queueing system Kendall models is named in the form A/S/c/K/N/D, where the slots are:
| Slot | Symbol set | Meaning |
|---|---|---|
A | M, D, G | Arrival process. M = Markovian (Poisson), D = deterministic, G = general |
S | M, D, G | Service-time distribution. Same alphabet as A |
c | integer ≥ 1 | Number of identical servers |
K | integer or ∞ | Queue capacity (defaults to ∞ if omitted) |
N | integer or ∞ | Population size (defaults to ∞ if omitted) |
D | FCFS / LCFS / SIRO / PS | Service discipline (defaults to FCFS / first-come, first-served if omitted) |
In practice the first three slots carry almost all of the meaning. Kendall's engine works in M/M/c, M/G/c, and M/M/c/K; the others are future work.
The notation was introduced by David G. Kendall in 1953. It survives as the lingua franca of queueing analysis because it cleanly separates the arrival process, the service process, and the system's structural limits — the three things you need to specify before any closed-form result will tell you anything.