Operations Research Models and Methods / Computation

Queueing Add-in


Non-Markovian User Functions

 

A second set of user functions is provided to analyze non-Markovian queueing station. They are similar to those for Poisson systems except they compute approximate values. Since the approximations are not valid for systems with finite populations or finite queues, the last two parameters are redefined to be the COV or arrivals and the COV of departures. Thus for each function we have the parameters:

(arrival rate, service rate, number of servers, COV of interarrival times, COV of service times)

The functions require that parameters be provided by using a range holding these values in the proper order. When a non-Markovian station is defined, the range holding the five numbers is given the Excel name which is the same as the Queue name given in the dialog box. On the last page we had an example station called PP1_2. The range D3:D7 holds the five parameters of that station and have the Excel name PP1_2. For the example the parameters are:

(8.5, 10, 1, 1, 0.5)

To compute the type of the queue we use the user function:

Type_NM(PP1_2).

The complete set of Non-Markovian functions are listed below with their values computed, to 3 place accuracy, for the station PP1_2.


Function

Notation

Result

Q_type_NM(PP1_2):
Determines the type of queue using Kendall's notation.

Type =

M/G/1

Q_L_NM(PP1_2):
Computes the mean number in the system.

L=

3.860

Q_W_NM(PP1_2):
Computes the mean number in the system.

W =

0.454

Q_Lq_NM(PP1_2):
Computes the mean number in the queue.

Lq=

3.010

Q_Wq_NM(PP1_2):
Computes the mean time in the queue.

Wq =

0.354

Q_Ls_NM(PP1_2):
Computes the mean number in service.

Ls=

0.85

Q_Ws_NM(PP1_2):
Computes the mean time in service.

Ws =

0.1

Q_Eff_NM(PP1_2):
Computes the efficiency of the servers.

Eff =

0.85

Q_COV_NM(PP1_2):
Computes the departure COV of the station.

COV =

0.677

Queueing Networks

Operations Research Models and Methods
by Paul A. Jensen and Jon Bard, University of Texas, Copyright by the Authors