M/M/1/4 vs M/M/2/4 queue

[mari_tsa]

Here is the code I wrote which is explained in comments.
% system M/M/1/4
% when there are 3 clients in the system, the capability of the server
doubles.

clc;
clear all;
close all;

lambda = 4;
mu = 5;
states = [0,1,2,3,4]; % system with capacity 4 states
% the initial state of the system. The system is initially empty.
initial_state = [1,0,0,0,0];

% define the birth and death rates between the states of the system.
births_B = [lambda,lambda,lambda,lambda];
deaths_D = [mu,mu,2*mu,2*mu];

% get the transition matrix of the birth-death process
transition_matrix = ctmcbd(births_B,deaths_D);
% get the ergodic probabilities of the system
P = ctmc(transition_matrix);

% plot the ergodic probabilities (bar for bar chart)
figure(1);
bar(states,P,"r",0.5);

% transient probability of state 0 until convergence to ergodic probability.
Convergence takes place P0 and P differ by 0.01
index = 0;
for T=0:0.01:50
  index = index + 1;
  P0 = ctmc(transition_matrix,T,initial_state);
  Prob0(index) = P0(1);
  if P0-P < 0.01
    break;
  endif
endfor

T = 0:0.01:T;
figure(2);
plot(T,Prob0,"r","linewidth",1.3);

If I had 2 servers thus a M/M/2/4 queue, what would have changed? How 2
servers would have affected the code ?
 In my opinion, it would make any difference, but is that true?



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