Python code to compute the blocking probability P
in the Engset model:
m
binom{N - 1}{m}M E/N
P = -------------------------- where M = ---------------.
__ m X 1 - E/N(1 - P)
\ binom{N - 1}{X}M
/__ X = 0
N
denotes the number of sources, m
the number of servers, and E
the offered traffic from all sources.
E
is the total offered traffic given by E = N * alpha
, where alpha
is the offered traffic per-source.
pip install fast_engset
from fast_engset import fe
m = 5 # Number of servers
N = 10 # Number of sources
alpha = 0.2 # Offered traffic from a SINGLE source
E = N * alpha # Total offered traffic from ALL sources
# Blocking probability
P = fe.compute(m, N, E)
If you are using this in an academic work, please cite the corresponding paper:
@article {MR3503106,
AUTHOR = {Azimzadeh, P. and Carpenter, T.},
TITLE = {Fast {E}ngset computation},
JOURNAL = {Oper. Res. Lett.},
FJOURNAL = {Operations Research Letters},
VOLUME = {44},
YEAR = {2016},
NUMBER = {3},
PAGES = {313--318},
ISSN = {0167-6377},
CODEN = {ORLED5},
MRCLASS = {90B22 (60K30)},
MRNUMBER = {3503106},
MRREVIEWER = {Vyacheslav M. Abramov},
DOI = {10.1016/j.orl.2016.02.011},
URL = {http://dx.doi.org/10.1016/j.orl.2016.02.011},
}