the performance of static VPN packets

For delay issues, we consider the performance of static VPNpackets. In static VPN lightpaths, some are dedicated andsome are shared. We consider shared static lightpaths. Adedicated path is just a special case of a shared one. In thistype of VPN lighpath, several VPN traffic streams shareone single-hop lightpath. We schedule the packets indifferent VPNs in a round-robin fashion. We treat theshared lightpath as a single server which serves V VPNtraffic streams, with the mean service time being 1/m.Furthermore, we assume the arrival of the packets fromdifferent VPNs are independent and we can calculate theequivalent service time for each VPN traffic. We can thenisolate each VPN traffic and model them as V independentM/G/1 queues, each with arrival rate lv ¼ l/V. Consider onetagged queue. Let m denote its mean service time and M2 beits second moment. Then its utilisation is rv ¼ lvm.Assuming that a message reaches the front of the queueimmediately after the node transmits the previous packet,the service time can be obtained as S ¼ Ly+y, where y isthe packet transmission time (i.e 1/m). Let L be the numberof non-empty VPN queues other than the tagged one.Assuming Poisson arrival and that the various VPNstreams are independent of each other, then L is binomialwith parameters (V1, rv). Hence, the expectation of S ism ¼ ðV  1Þrvy þ y ð2Þand its second moment isM2 ¼ðV  1Þy2ðrvð1  rvÞ þ  ðV  1Þr2vÞþ 2ðV  1Þrvy2 þ y2ð3Þwhere y2 is the second moment of y.