OPTIMIZATION SEMINAR
A Critically Loaded Multirate Link with Trunk Reservation
Tolya Puhalskii
University of Colorado at Denver
Department of Mathematics
Tuesday, Nov. 25, 1997, 12:00 noon
CU-Denver Bldg., Room 626
ABSTRACT:
We consider a loss system model of interest in
telecommunications.
There is a single service facility with a number of servers
in parallel and no waiting room.
There are several types of arriving customers, with each type
requiring a certain number of servers simultaneously.
We consider the trunk reservation acceptance policy when
an arriving customer of a given type is accepted only if
the number of idle servers is not less than a certain number
which is generally greater than the number of servers required
to serve this type of customers.
We examine the asymptotic behavior of the system in the
regime known as critical loading
and prove that the multidimensional `queue length' process
converges, under the appropriate normalization, to a
particular multidimensional diffusion.
For the associated optimization
problem where accepted customers pay, we show that
our trunk reservation
policy is asymptotically optimal when the parameters satisfy a
certain relation.