MSMQ-Example
The MSMQ-example describes a multiserver multiqueue system with
finite capacity queues. The example has been first published as a Petri-Net
model in [1] and is afterwards used in many papers as a reference example.
APNN-Description
The model is described as a hierarchical net with 5 subnets. Communication
between subnets is asynchronous and describes the movement of tokens from
one queue to another. The hierarchical description corresponds to a partition
of the set of places such that each subnet specifies one automaton/component
of the net. The transitions visible in the upper level are all synchronized
transitions, the remaining transitions inside the subnets are local.
The state space size of the model is scalable by modifying the number
of queues, which requires to generate new subnets, by the number of servers,
which can be done by adding and removing tokens from place p4 of subnet
1, and by the size of the queues, which can be modified by adding/removing
tokens from place p1 in every subnet.
In the current version of have 5 queues of capacity 6 and 3 servers.
Automata-Description
The automata description of the example includes the matrices for a model
with the above mentioned parameters which results in a CTMC with 2,945,880
reachable states and 19,894,875 transitions.
- Matrices of the flat automata network
with a potential state space including 777,600,000 states.
- Matrices of the hierarchical
automata network with 35 states in the upper level and a potential state
space that is identical to the reachable state space.
References
- M. Ajmone-Marsan, S. Donatelli, F. Neri: GSPN models of Markovian
multiserver mutiqueue systems. Performance Evaluation 11, 1990, pp. 227-240.