Solving the Model

For this model, we will give special attention on how to use an approximation technique to calculate the Expected Cumulative Rate Reward (ESRA). For more references about this method see [#!PMCCS4!#].

We have to specify a measure of interest using rewards. In this example, we can specify the total time an object holds the token, using a rate reward in the Reward's attribute:

rate_reward  = token_queue_1
   condition = (token == 1)
   value     = 1;

It is possible to compute the expected cumulative rate reward for a subset of states. The subset of states has to be specified using the global reward object. Only the objects that satisfy the global reward condition will be included in the subset. In this example, we want to consider all states so the syntax of the global reward is the following:

global_rewards=
rate_reward  = states
   condition = (TRUE)
   value     = 1;

To solve the model, click on the Analytical Model Solution button. Choose the Transient $\rightarrow$ Expected Values $\rightarrow$ ESRA $\rightarrow$ Direct Technique.

In the next step, we input the following parameters: Initial Probability, Time Intervals, Total number of Erlang Stages, Block Set (in this method the matrix is block-partitioned) and the Measure of Interest.

Initial Probability : Initial State
Time Intervals      = 5 1 
Erlang Stages       = 10
Block Set           = 1 29 1
Measure of Interest = Set Reward
Reward Name         = 
   multiplex_channel.rate_reward.Queue1.token_queue_1

(See [#!PMCCS4!#] for more information about the Erlang Stages parameter.) The result is printed in the file
Multiplex_Channel.TS.DIRECT.Cumulative_SET_Reward.
This file has some information about the parameters considered in the solution and the expected rate reward accumulated at each time interval in the subset of states. In this example, the rate reward is the total time queue 1 holds the token.