COMPACT MODELS OF RANDOM POLLING SYSTEMS - Modelling with Generalised Stochastic Petri Nets - page 205

service disciplines is irrelevant for systems where the storage capacity
at all queues is 1
• the polling order, which defines the sequence according to which the
server visits the queues; the normal polling order is cyclic, but other
polling orders are also interesting: for example, with the random order,
the next queue to be visited is selected at random among all queues,
including the one just visited
• the server walk times from one queue to the next, which can be random
variables with general distributions
While traditional polling models consider the availability of only one server,
a new emerging area of interest is the one of multiserver polling models, also
called multiserver multiqueue (MSMQ) systems.
The description of the behaviour of a multiserver polling system requires the
definition of the same elements that we listed above for single-server polling
systems, together with some new aspects:
• the number of servers
• the server utilization policy, which defines the maximum number of
servers that can be simultaneously attending a queue; the distinction
among server utilization policies is irrelevant in the single-server case,
as well as for systems where the storage capacity at all queues is 1
The research on MSMQ systems started only recently, so that the literature
is rather scarce: some papers that deal with MSMQ systems, both from a
theoretical and from an applicative point of view, are [ 52] - [45] . Some of the
first exact numerical results for MSMQ systems were obtained with GSPN
models: for example, in [ 44] , MSMQ systems with cyclic polling order were
analysed.
Here we consider multiserver polling models where:
• the number of queues is equal to N ( ≥ 1)
• the storage capacity at each queue is equal to 1
• the customer arrival process at each queue is Poisson with rate λ, with
interruptions due to the limited storage capacity
• the number of servers is equal to S (1 ≤ S ≤ N)
• at each queue, for each server, the customer service times are indepen-
dent, exponentially distributed random variables with mean 1/µ