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Written By Dr. Victor S. Frost
Dan F. Servey Distinguished Professor
Electrical Engineering and Computer Science
University of Kansas

Find the system size to meet  blocking probability specification, Pspec.
Results are system size and blocking probability.
MaxSystemSize is the maximum system size that will be considered.

Pspec=0.01;

MaxSystemSize=50;

Load for Erlang B and Erlang C

load=17.;

Load for M/M/1/S (Load for M/M/1/S must be < 1)

loadMM1S=0.5;

Erlang B

s1=Nearest[Table[ErlangB[M,load], {M, 1, MaxSystemSize}]->"Index",Pspec];
PErlangB=ErlangB[s1,load];
If[PErlangB[[1]]<Pspec, s1, s1+1]
ErlangB[If[PErlangB[[1]]<Pspec, s1, s1+1],load]

Erlang B: System size that meet Pspec

Erlang B: Probability of blocking given system size

Erlang C

s2=Nearest[Table[ErlangC[M,load], {M, 1, MaxSystemSize}]->"Index",Pspec];
PErlangC=ErlangC[s2,load];
If[PErlangC[[1]]<Pspec, s2, s2+1]
ErlangB[If[PErlangC[[1]]<Pspec, s2, s2+1],load]

Erlang C: System size that meet Pspec

Erlang C: Probability of delayed given system size

M/M/1/S system  load<1

Pdelay[N_]=(((1-loadMM1S)*(loadMM1S^N))/(1-(loadMM1S^(N+1))));
s3=Nearest[Table[Pdelay[N], {N, 1, MaxSystemSize}]->"Index",Pspec];
Pwait=Pdelay[s3];
If[Pwait[[1]]<Pspec, s3, s3+1]
ErlangB[If[Pwait[[1]]<Pspec, s2, s2+1],load]

M/M/1/S: System size that meet Pspec

M/M/1/S:  Probability of blocking given system size