PERFORMANCE MEASURES

This week we have to calculate performance measures for the restaurant HAMBURGER, but assuming that the distribution of the inter-arrival times and service times is exponential. This assumption is very important to apply Jackson’s theorem and modeling the system as a Jackson network.

Thus, by Jackson’s theorem, the arrival rates are calculated with the following expression:

The system of equations of the total arrival rates of HAMBURGER is:

 Looking at the graph schema, in “System Data” publication, the system of equations is simplified as it’s shown. 

We assume that our system satisfy Jackson’s suppositions (exponential inter-arrival times, exponential service times, infinite capacity for all stations and reached stable state λ_i<s_i*μ_i for all i stations). Then, the arrival rates found correspond to inter-arrival times distributed exponential. In order to calculate performance measures, we use network formulas, shown in the next table.

We hope you enjoyed our entry.

Thank you for reading us,

Nataly Patacón

Camila Fonseca

Fernand Malagón

Alejandro Moreno