Package jline.api.qsys

Class Qsys_mg1k_loss

java.lang.Object

jline.api.qsys.Qsys_mg1k_loss

public final class Qsys_mg1k_loss
extends Object

Method Summary

Modifier and Type	Method	Description
static HashMap<String,Object>	qsys_mg1k_loss(double lambda, DoubleUnaryOperator svc_density, int K)	Exact M/G/1/K loss probability via the Markov chain embedded at service-start epochs (transform-free analysis in the spirit of Niu-Cooper).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

qsys_mg1k_loss

public static HashMap<String,Object> qsys_mg1k_loss(double lambda,
 DoubleUnaryOperator svc_density,
 int K)

Exact M/G/1/K loss probability via the Markov chain embedded at service-start epochs (transform-free analysis in the spirit of Niu-Cooper).

State: number of customers waiting in the queue immediately after a service start, q in {0,...,K-2}. With a_j = P(j Poisson arrivals during a service time): from q=0, if no arrival occurs during the service the system empties and the next service starts with the next arrival (q'=0), so both a_0 and a_1 lead to q'=0 and j>=2 arrivals lead to q'=j-1; from q>=1, q'=q-1+j with arrivals beyond the free capacity lost (aggregated in the last column). The loss probability follows from the renewal-reward argument P_loss = 1 - 1/(rho + sigma_0*a_0), with sigma the stationary distribution at service-start epochs.

Reference: Niu, Cooper. Transform-Free Analysis of M/G/1/K and Related Queues. Mathematics of Operations Research 18(2), 1993, 486-510.