Call–burst blocking of ON–OFF traffic sources with retrials under the complete sharing policy

In this paper we calculate both call and burst blocking probabilities of ON–OFF traffic sources with retrials. Calls of service-classes arrive to a single link according to a Poisson process and compete for the available link bandwidth under the complete sharing policy. Blocked calls may immediately retry one or more times to enter the system, with reduced bandwidth and increased mean service time requirements. Call blocking occurs when a call cannot enter the system with its last bandwidth requirement, due to lack of bandwidth. Accepted calls enter the system via state ON and may alternate between states ON and OFF, or remain always in state ON. When a call is transferred to state OFF it releases the bandwidth held in state ON, so that this bandwidth becomes available to new arriving calls. When a call tries to return to state ON, it re-requests its bandwidth. If it is available a new ON-period (burst) begins. Otherwise burst blocking occurs and the call remains in state OFF. The proposed ON–OFF retry models do not have a product form solution and therefore the calculation of call and burst blocking probability is based on approximate formulas. The formulas we propose for the call blocking probabilities are recursive, whereas for the burst blocking probabilities are robust. Simulation results validate our analytical methodology. For further evaluation, the results of the ON–OFF retry models are compared with those of the ON–OFF model without retrials. We also discuss the extension of the proposed formulas in the case of a fixed-routing network.