m/m/1 queuing system -凯发k8网页登录

overview

this example shows how to model a single-queue single-server system with a single traffic source and an infinite storage capacity. in the notation, the m stands for markovian; m/m/1 means that the system has a poisson arrival process, an exponential service time distribution, and one server. queuing theory provides exact theoretical results for some performance measures of an m/m/1 queuing system and this model makes it easy to compare empirical results with the corresponding theoretical results.

structure

the model includes the components listed below:

entity generator block: models a poisson arrival process by generating entities (also known as "customers" in queuing theory).

simulink function exponentialarrivaltime(): returns data representing the interarrival times for the generated entities. the interarrival time of a poisson arrival process is an exponential random variable.

entity queue block: stores entities that have yet to be served in fifo order

entity server block: models a server whose service time has an exponential distribution.

results and displays

the model includes these visual ways to understand its performance:

scopes labeled "waiting time: theoretical" and "waiting time: simulation" showing the theoretical and empirical values of the waiting time in the queue, on a single set of axes. you can use this plot to see how the empirical values evolve during the simulation and compare them with the theoretical value.