Admission Control in Priority Queueing System With Servers Reservation and Temporal Blocking Admission of Low Priority Users

We analyse a cell of Cognitive Radio Network (
$CRN$
) as the multiline queueing system supplying service to two Markovian arrival flows of users. Primary (or licensed) users called as High Priority Users (
$HPU\text{s}$
) have a preemptive priority over the secondary (cognitive) users called as Low Priority Users (
$LPU\text{s}$
). The
$HPU\text{s}$
are dropped upon the arrival only if all servers are occupied by
$HPU\text{s}$
. If at the arrival epoch all servers are busy but some of them provide service to
$LPU\text{s}$
, service of one
$LPU$
is immediately interrupted and service of the
$HPU$
begins in the released server. A
$LPU$
is accepted only if the number of busy servers at arrival epoch is less than the defined in advance threshold
$M$
. Otherwise, the
$LPU$
is permanently lost or becomes a retrial user. A retrial user repeats attempts to receive service later after random time intervals. The
$LPU$
whose service is interrupted is either lost or transferred to a virtual place called as orbit. The users placed in the orbit may be impatient and can renege the system. The service time follows an exponential probability distribution with the rate determined by the user’s type. After loss of a
$HPU$
, admission of
$LPU\text{s}$
is blocked.
$LPU\text{s}$
are informed that their access is temporarily suspended and do not generate new requests until blocking expires. The purpose of the research is the optimization of threshold
$M$
and admission blocking period duration. Behavior of the system is described by a multidimensional continuous-time Markov chain. Its generator, ergodicity condition and invariant distribution are derived. Expressions for performance indicators are given. Numerical results demonstrating usefulness of blocking and significance of account of correlation in arrivals are presented. E.g., in the presented example of cost criterion optimization blocking gives 18 percent profit comparing to the system without blocking.