pfqn_ssd.h File Reference

Server-Station Disaggregation bounds for a multiserver closed network (Dallery and Suri, SIGMETRICS 1986). More...

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

Include dependency graph for pfqn_ssd.h:

Go to the source code of this file.

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

Namespaces
namespace	line
namespace	line::pfqn

Functions
template<class T>
SsdBounds< T >	line::pfqn::pfqn_ssd (const std::vector< T > &L, const T &N, const T &Z, const std::vector< T > &nservers)
	Server-Station Disaggregation bounds for a multiserver closed network (Dallery and Suri, SIGMETRICS 1986).
template<class T>
SsdBounds< T >	line::pfqn::pfqn_ssd (const std::vector< T > &L, const T &N, const T &Z)

Detailed Description

Server-Station Disaggregation bounds for a multiserver closed network (Dallery and Suri, SIGMETRICS 1986).

Templated port of matlab/src/api/pfqn/pfqn_ssd.m. Single-class model: L is the per-station demand vector, N the population, Z the think time.

Theorem 5 eq. (6) carries no think time of its own. The objection this file used to raise still stands as far as it went: inserting a bare +Z into the Theorem 5 form is NOT a bound, because the BJB optimistic step needs sum_k Q_k(N-1) = N-1, which fails once Z X(N-1) jobs sit at the terminal. What that argument missed is that the queueing term can be corrected instead of the delay being disaggregated separately. The reference now scales it by the terminal-workload factor of Lazowska et al. 1984, Table 5.2: (N-1) Y_l / (1 + Z/(N R_l)) on the lower bound and (N-1) Y_u / (1 + Z/R_u) on the upper. Both reduce to the Z=0 forms exactly, so this generalises rather than replaces eq. (6), and the Z>0 case is computed instead of refused.

All operations stay in the field, so the bound is exact in rational arithmetic: a bound computed exactly is worth having, since a bound violated only by rounding is indistinguishable from a real violation.

Definition in file pfqn_ssd.h.