# MARCA_Models:

LEAKY --- A Leaky Bucket Model

# William J. Stewart

## A Leaky Bucket Model

A "leaky-bucket" model of the type used in telecommunication
modelling. This is basically a queueing system with a finite
buffer and two type of customers; the first arrive
according to a Poisson distribution and the second at fixed
intervals of time.

The leaky bucket model is designed to help in determining
the dimensioning of intermediate buffers in ATM telecommunication networks. The leaky bucket model consists of a buffer area into which a nondeterministic flow is presented, but which
empties itself at a constant rate. The external arrival flow
consists of several sources, one of which is isolated from
the others. These others are modeled by a single Poisson
process at rate * lambda. *

The arrival process is therefore of type * (M+T)/D/1/C
* The capacity of the queue is * C * cells.
The arrival process of the marked cells is periodic of
period * T D * where * T * is an integer.

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Values of T, C, n and nz for the 17 datasets:
T C n nz
4 64 8,258 197,474
8 64 16,578 397,150
12 64 24,898 596,826
16 64 33,218 796,502
24 64 49,858 1,195,854
32 64 66,498 1,595,206
40 64 83,138 1,994,558
48 64 99,778 2,393,910
60 64 124,738 2,992,938
64 64 133,058 3,192,614
12 100 60,502 2,176,344
24 100 121,102 4,357,932
32 100 161,502 5,812,324
48 100 242,302 8,721,108
64 100 323,102 11,629.892
96 100 484,702 17,447,460
100 100 504,902 18,174,656
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