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The Poisson process and exponentially distributed service time

The Poisson process and exponentially distributed service time In real life customers don’t arrive at pre-ordained times as

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The Poisson process and exponentially distributed service time

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  1. The Poisson process and exponentially distributed service time In real life customers don’t arrive at pre-ordained times as specified in the last tutorial… A more realistic approach is to model the number of arrivals in any given interval of time as being a random quantity governed by some probability distribution. The most common one to use is the Poisson process which says that the probability of k customers arriving in t units of time is given by The quantity is the mean (average) rate at which customers arrive per unit time.

  2. To set up the source in our Workbench simulation as a Poisson process we specify the number of customers (transactions) created per time unit as poisson(lambda) where lambda is the average number of arrivals per time-unit. Here I have set up a Poisson process with an average of 0.5 customers created per module unit.

  3. The Poisson distribution is a discrete probability distribution. It tells us the probability of 0,1,2,3 …. customers arriving over a time - period. Service time is a continuous quantity however. Service time can range anywhere in the interval Real-life service times can often be described by an exponential probability distribution. The exponential distribution says that the probability that the service time is less than T (where T>0) is The average service time can be shown to be equal to which means that on average customers get served per time-unit. The rate at which people are served can therefore be thought of a Poisson process with mean .

  4. Here I have graphed P(t < x) for various values of The blue line is and mean service time is 0.5 The red line is and mean service time is 1.0 The green line is and mean service time is 2.0

  5. To set up our service node as a Poisson process we specify the service time as having an exponential distribution with parameter mu. The syntax is expo(mu) Here I have set up a Poisson process with an average of 1.0 customers served per module unit.

  6. Now you can begin to reproduce some of the results we derived analytically in class. You can set the quantity by choosing appropriate expressions in the source and server nodes. A few more points: A finite queue server can be set up by using the finite queue tab to the right.. Choose finite queue service… In the service node specifications ‘type’ tab you can set the maximum capacity of this node to be a predefined constant by altering the queue_node_capacity value found in the ‘variables’ sub-tab.

  7. You can also change the number of servers by choosing the service node specifications ‘instance’ tab and changing the value of servers…

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