qbd_bmapbmap1.m

%{ @file qbd_bmapbmap1.m
 %  @brief Computes QBD blocks for a BMAP/BMAP/1 queue
 %
 %  @author LINE Development Team
%}
 
%{
 % @brief Constructs QBD blocks for batch arrival/service queue
 %
 % @details
 % This function computes the QBD (Quasi-Birth-Death) transition blocks
 % for a BMAP/BMAP/1 queue with batch arrivals and batch service.
 %
 % @par Syntax:
 % @code
 % qbd_bmapbmap1(MAPa, pbatcha, MAPs)
 % @endcode
 %
 % @par Parameters:
 % <table>
 % <tr><th>Name<th>Description
 % <tr><td>MAPa<td>Arrival process (MAP)
 % <tr><td>pbatcha<td>Probability distribution of batch sizes
 % <tr><td>MAPs<td>Service process (MAP)
 % </table>
 %
 % @par Returns:
 % <table>
 % <tr><th>Name<th>Description
 % </table>
%}
function qbd_bmapbmap1(MAPa, pbatcha, MAPs)
na = length(MAPa{1});
ns = length(MAPs{1});
maxbatch = length(pbatcha);
 
for b=1:maxbatch
    A1{b} = kron(MAPa{2}*pbatcha(b),eye(ns));
end
A0 = krons(MAPa{1},MAPs{1});
A_1 = kron(eye(na),MAPs{2});
A0bar = kron(MAPa{1},eye(ns));
B0 = krons(MAPa{1},eye(ns));
for b=1:maxbatch
    B1{b} = kron(MAPa{2}*pbatcha(b),eye(ns));
end
 
% first few levels of Q matrix
%Z = 0*B0;
%Q=[B0,cell2mat(B1),Z,Z,Z;
% A_1,A0,cell2mat(A1),Z,Z;
% Z,A_1,A0,cell2mat(A1),Z;
% Z,Z,A_1,A0,cell2mat(A1)];
 
end