cache_ttl_lrum.m

%{ @file cache_ttl_lrum.m
 %  @brief Computes steady-state probabilities for TTL-based LRU(m) cache
 %
 %  @author LINE Development Team
%}
 
%{
 % @brief Computes steady-state probabilities for LRU(m) cache
 %
 % @details
 % This function computes the steady-state probability distribution for a
 % TTL-based LRU(m) cache system.
 %
 % @par Syntax:
 % @code
 % prob = cache_ttl_lrum(gamma, m)
 % @endcode
 %
 % @par Parameters:
 % <table>
 % <tr><th>Name<th>Description
 % <tr><td>gamma<td>Arrival rates per item per list
 % <tr><td>m<td>Cache capacity vector
 % </table>
 %
 % @par Returns:
 % <table>
 % <tr><th>Name<th>Description
 % <tr><td>prob<td>Steady-state probability distribution
 % </table>
%}
function prob=cache_ttl_lrum(gamma,m)
gamma = gamma(1,:,2:end);
gamma = reshape(gamma,size(gamma,2),size(gamma,3));
[n,h]=size(gamma);
t = cache_t_lrum(gamma,m);  % the characteristic time of each list, a total of h lists
 
probh = zeros(n,h);   % steady state 1,...,h
prob0 = zeros(n,1);   % steady state 0
trans = zeros(n,h);
denom = zeros(1,n);
 
for k =1:n
    for j = 1:h
        trans(k,j) = exp(gamma(k,j)*t(j))-1;  %birth and death
    end
    denom(k) = sum(cumprod(trans(k,:)));
end
 
for k = 1:n
    for l = 1:h
        probh(k,l) = prod(trans(k,1:l))/(1+denom(k));
    end
    prob0(k) = 1-sum(probh(k,:));
end
prob = [prob0 probh];
end