pfqn_lcfsqn_ca.h File Reference

Convolution algorithm for the two-station multiclass LCFS queueing network of Casale, "A family of multiclass LCFS queueing networks with order-dependent product-form solutions", QUESTA 2026. More...

#include <cstddef>
#include <vector>
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/matrix.h"
#include "line/util/population.h"

Include dependency graph for pfqn_lcfsqn_ca.h:

Go to the source code of this file.

Classes
struct	line::pfqn::LcfsQnResult< T >

Namespaces
namespace	line
namespace	line::pfqn

Functions
template<class T>
LcfsQnResult< T >	line::pfqn::pfqn_lcfsqn_ca (const std::vector< T > &alpha, const std::vector< T > &beta, const std::vector< int > &N)
	Convolution algorithm for the two-station multiclass LCFS queueing network of Casale, "A family of multiclass LCFS queueing networks with order-dependent product-form solutions", QUESTA 2026.

Detailed Description

Convolution algorithm for the two-station multiclass LCFS queueing network of Casale, "A family of multiclass LCFS queueing networks with order-dependent product-form solutions", QUESTA 2026.

Templated port of matlab/src/api/pfqn/pfqn_lcfsqn_ca.m.

Station 1 is LCFS (non-preemptive) and station 2 is LCFS-PR (preemptive-resume); alpha_r and beta_r are the class-r mean service times at the two stations. The network is NOT product form in the classical sense – the balance function depends on the ORDER of the jobs in the LCFS queue, not only on their counts – so the constant obeys a coupled pair of recursions over the population lattice rather than a single Buzen update:

V(0) = 1, V(n) = prod_r alpha_r^{n_r} * sum_{r: n_r > 0} V(n - e_r) G(0) = 1, G(n) = sum_{r: n_r > 0} alpha_r^{|n|-1} beta_r G(n - e_r) + V(n)

V is the order-dependent auxiliary term contributed by the non-preemptive station; it is returned alongside G because the mean-value routine pfqn_lcfsqn_mva needs it.

Arithmetic: EXACT-CAPABLE. Only integer powers, additions and multiplications in the field of the inputs.

Definition in file pfqn_lcfsqn_ca.h.