Jackson Networks Independent external Poisson arrivals Independent Exponential service times Same job has independent service time at different queues Independent routing of packets When a packet leaves node i it goes to node j with probability Pi Packet leaves system with probability 1 Packets can loop inside network Arrival rate at node i, + k ki External Internal arrivals from arrivals Other nodes Set of equations can be solve to obtain unique ns Service rate at node i= HiJackson Networks • Independent external Poisson arrivals • Independent Exponential service times – Same job has independent service time at different queues • Independent routing of packets – When a packet leaves node i it goes to node j with probability Pij – Packet leaves system with probability 1 −=∑j Pij – Packets can loop inside network • Arrival rate at node i, λi = ri +=∑k λk Pki External Internal arrivals from arrivals Other nodes – Set of equations can be solve to obtain unique λi’s – Service rate at node i = µi Eytan Modiano Slide 9