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 (<inline-formula> <tex-math notation="LaTeX">$CRN$ </tex-math></inline-formula>) as the multiline queueing system supplying service to two Markovian arrival flows of users. Primary (or licensed) users called as High Priority Users (<inline-formula> <tex-math notation="LaTeX">$HPU\text{s}$ </tex-math></inline-formula>) have a preemptive priority over the secondary (cognitive) users called as Low Priority Users (<inline-formula> <tex-math notation="LaTeX">$LPU\text{s}$ </tex-math></inline-formula>). The <inline-formula> <tex-math notation="LaTeX">$HPU\text{s}$ </tex-math></inline-formula> are dropped upon the arrival only if all servers are occupied by <inline-formula> <tex-math notation="LaTeX">$HPU\text{s}$ </tex-math></inline-formula>. If at the arrival epoch all servers are busy but some of them provide service to <inline-formula> <tex-math notation="LaTeX">$LPU\text{s}$ </tex-math></inline-formula>, service of one <inline-formula> <tex-math notation="LaTeX">$LPU$ </tex-math></inline-formula> is immediately interrupted and service of the <inline-formula> <tex-math notation="LaTeX">$HPU$ </tex-math></inline-formula> begins in the released server. A <inline-formula> <tex-math notation="LaTeX">$LPU$ </tex-math></inline-formula> is accepted only if the number of busy servers at arrival epoch is less than the defined in advance threshold <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>. Otherwise, the <inline-formula> <tex-math notation="LaTeX">$LPU$ </tex-math></inline-formula> is permanently lost or becomes a retrial user. A retrial user repeats attempts to receive service later after random time intervals. The <inline-formula> <tex-math notation="LaTeX">$LPU$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$HPU$ </tex-math></inline-formula>, admission of <inline-formula> <tex-math notation="LaTeX">$LPU\text{s}$ </tex-math></inline-formula> is blocked. <inline-formula> <tex-math notation="LaTeX">$LPU\text{s}$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> 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.