First Passage Times in M2[X]|G|1|R Queue with Hysteretic Overload Control Policy

One of the reported approaches towards the solution of overload problem in networks of SIP servers is the implementation of multi-level hysteretic control of arrivals in SIP servers. Each level, being the parameter of the policy, specifies operation mode of SIP server i.e. it implicitly indicates what SIP server must do with the arriving packets. The choice of parameters' values is not guided by standards and is usually left for the network owner. In general, all operation modes of the considered policy can be grouped into two groups: normal mode (when all arriving packets are accepted) and congested mode (when part or all arriving packets are being dropped). Such grouping may serve as the criteria for choosing parameters' values of the policy: pick those values which minimize SIP server sojourn time in congested mode. In this short note we propose some analytical results which facilitate the solution of stated minimization problem. The considered mathematical model of SIP server is the queueing system M-2([X])vertical bar G vertical bar 1 vertical bar R with batch arrivals and bi-level hysteretic control policy, which specifies three operation modes: normal (customers both flows are accepted), overload (only customers from one flow are accepted), discard (customers from both flows are blocked/lost)). The switching between modes can occur only on service completions. Analytical method allowing computation of stationary sojourn times in different operation modes (as well as first passage times between modes) is presented in brief. Numerical example is given.