Qsys_gigk_approx_cosmetatos (LINE Solver Java API)

java.lang.Object

jline.api.qsys.Qsys_gigk_approx_cosmetatos

public final class Qsys_gigk_approx_cosmetatos extends Object

Method Summary

Modifier and Type

Method

Description

static HashMap<String,Object>

qsys_gigk_approx_cosmetatos(double lambda, double mu, double ca, double cs, int k)

GI/G/k approximation by interpolation of the M/M/k, M/D/k and D/M/k queues (Cosmetatos 1982; Page 1982): Wq = [ca^2*cs^2 + ca^2*(1-cs^2)*phi1/2 + (1-ca^2)*cs^2*phi3/2]*Wq(M/M/k), where phi1 and phi3 are the Cosmetatos (1975) correction factors for M/D/k and D/M/k, with the safeguards of Whitt (1993).

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details
- qsys_gigk_approx_cosmetatos
  
  public static HashMap<String,Object> qsys_gigk_approx_cosmetatos(double lambda, double mu, double ca, double cs, int k)
  
  GI/G/k approximation by interpolation of the M/M/k, M/D/k and D/M/k queues (Cosmetatos 1982; Page 1982): Wq = [ca^2*cs^2 + ca^2*(1-cs^2)*phi1/2 + (1-ca^2)*cs^2*phi3/2]*Wq(M/M/k), where phi1 and phi3 are the Cosmetatos (1975) correction factors for M/D/k and D/M/k, with the safeguards of Whitt (1993). The D/D/k corner has Wq=0. The interpolation requires ca^2<=1 and cs^2<=1; outside this region the Lee-Longton scaling Wq = ((ca^2+cs^2)/2)*Wq(M/M/k) is used.
  References: Cosmetatos, G.P. (1975). Approximate explicit formulae for the average queueing time in the processes (M/D/r) and (D/M/r). INFOR 13, 328-331. Page, E. (1982). Tables of waiting times for M/M/n, M/D/n and D/M/n and their use to give approximate waiting times in more general queues. J. Opl. Res. Soc. 33, 453-473.
  
  Parameters:
  
  lambda - arrival rate
  
  mu - service rate per server
  
  ca - coefficient of variation of inter-arrival time
  
  cs - coefficient of variation of service time
  
  k - number of servers
  
  Returns:
  
  HashMap containing W (mean response time), rhohat (modified utilization so that M/M/1 formulas still hold), plus L, Q, U