After describing the model, we can obtain different measures of interest using rate or s. Rate rewards are associated with the states in the model. These rewards are generic enough to permit the definition of a wide range of measures of interest. (For references on reward models and some of the techniques implemented, see [#!deso89!#,#!deso-perfsurv!#,#!trans-finalg98!#].)
If a is associated with state
, them the system
gains reward
per time unit spent in state
. Impulse rewards are
associated with state transitions. If a reward
is associated
with the transition from state
to
, then the system gains a reward
each time it makes a transition from
to
. The
s may be used as a counting mechanism. An impulse reward
can be associated with the triggering of an event, or with the reception of a
message.
Below, we illustrate the use of rewards with the M/M/1/k model. Return to the ``Model Specification Module'', and open our model (using TGIF). We specify the rewards using the Rewards attribute:
Rewards= rate_reward = <name of reward> condition = value = ;Suppose that we are interested in calculating the utilization of the queue in the Server_Queue object. We can define a reward variable utilization that can express this measure of interest. The user should specify the name of the reward, used as an identifier. The condition identifies the subset of states that will be associated with the reward. The reward value is specified in value. If the condition is not satisfied, that means we are not in our chosen subset of states and a reward of 0 is given.
Rewards= rate_reward = utilization condition = (Queue > 1) value = 1.0;The expected value of the queue size can be specified as a as follows:
Rewards= rate_reward = q_size condition= (TRUE) value= queue;Note that the total accumulated reward in
Suppose now we are interested in counting the number of customers served in
. An can be associated with the event
Packet_Service and defined to have a value of 1 when this event
triggers. We have:
Rewards= impulse_reward = served event= Packet_Service,1 value= 1;Clearly the accumulated impulse reward in
Figure shows the model and the objects
attributes specified.
Guilherme Dutra Gonzaga Jaime 2010-10-27