Package jline.api.qsys

Class Qsys_erlanga

java.lang.Object
jline.api.qsys.Qsys_erlanga
public final class Qsys_erlanga extends Object
Exact analysis of the Erlang A model M/M/s/r+M.

Poisson arrivals at rate lambda, exponential service of rate mu at each of s servers and exponential patience of rate theta, so a waiting customer abandons after an exponential time of mean 1/theta. The number in system is the birth-and-death process with birth rate lambda and death rate min(k,s)*mu + (k-s)^+ *theta, so every measure is EXACT: this is the special case in which the state-dependent Markovian approximation of Qsys_mgisrgi_whitt reproduces the model rather than approximating it (eq. 7.12 of the reference). theta > 0 makes the model ergodic at every load, including lambda above s*mu.

Port of MATLAB qsys_erlanga.m.

Reference: W. Whitt (2005). Engineering solution of a basic call-center model. Management Science 51(2), 221-235, Section 7 and eq. (7.12). The model itself is due to C. Palm (1937, 1957).

Since:
LINE 3.1.0

  • Method Details

    • qsys_erlanga

      public static QsysAbandonResult qsys_erlanga(double lambda, double mu, double theta, int s)
      Erlang A with an infinite waiting room.
      Parameters:
      lambda - arrival rate
      mu - service rate of one server
      theta - abandonment rate of a waiting customer
      s - number of servers
      Returns:
      the steady-state measures

    • qsys_erlanga

      public static QsysAbandonResult qsys_erlanga(double lambda, double mu, double theta, int s, double r)
      Erlang A with r extra waiting spaces, so an arrival finding s+r customers is blocked and lost.
      Parameters:
      lambda - arrival rate
      mu - service rate of one server
      theta - abandonment rate of a waiting customer
      s - number of servers
      r - extra waiting spaces, Double.POSITIVE_INFINITY if unbounded
      Returns:
      the steady-state measures

    • qsys_erlanga

      public static QsysAbandonResult qsys_erlanga(double lambda, double mu, double theta, int s, double r, double[] wPoints)
      Erlang A, with the waiting-time cdfs when times are supplied.
      Parameters:
      lambda - arrival rate
      mu - service rate of one server
      theta - abandonment rate of a waiting customer
      s - number of servers
      r - extra waiting spaces, Double.POSITIVE_INFINITY if unbounded
      wPoints - times at which to evaluate the waiting-time cdfs, or null
      Returns:
      the steady-state measures