Optimal call routing in VoIP

We evaluate from a VoIP provider's point of view possible strategies for selecting PSTN gateways and/or signaling servers (perhaps through ENUM) under blocking uncertainty. Each alternative can have different price for a terminating VoIP call and different blocking probability. A customer placing a call to the VoIP provider is impatient and may hang-up if the delay in setting up the call is large. Possible strategies for completing the call include routing the call to the gateway which generates maximum expected revenue from the call, or simultaneously to a set of gateways charging different prices possibly, a strategy called `forking'. Forking creates a race between the gateways who are trying to terminate the call and thus reduces the average call setup delay, but at the expense of increasing the average termination cost and the overall load of the system. For the above strategies we investigate the trade-off between the average profit generated by a call and call setup delay. We obtain under several assumptions the optimal set of gateways to which to send a call request. We also discuss the effects of forking on the overall call blocking probability of the system and the incentives for gateways and VoIP providers to deploy it. Our results suggest that if forking is enabled then it can be advantageous for gateways to introduce a small signaling charge.