G-networks with multiple classes of negative and positive customers

Some Applications of Multiple Classes G-Networks with Restart

“…The service rates do not depend on the queue. They are equal to μ (1) for type 1 and μ (2) for type 2. For the sake of simplicity, we assume here that the service distributions are exponential.…”

“…ρ 2 = ρ) and we assume that the overhead is the load of the queues due to the migration (i.e. ρ (2) 1 + ρ (2) 2 ). Assuming that the system is balanced, we have:…”

“…Since the seminal papers [2,5,6] published by Gelenbe more than 20 years ago, G-networks of queues have received considerable attention. G-networks have been previously presented to model Random Neural Networks [7,8].…”

“…Taking now the other part of the objective into account we want to minimize the overhead of the load balancing mechanism. Remember that the global overhead is: (2) .…”

Analysis of stochastic Petri nets with signals

“…In fact, as observed in [16], these mechanisms can indeed be useful for representing certain token movements in stochastic Petri nets. Other extensions are important in queueing network theory, particularly those with multiple classes of positive customers or signals [11,21] and the so-called reset customers of [19,29]. Resets move from one node to another and, on arriving at an empty queue, change the number of enqueued customers from zero to some random value that has a probability distribution that coincides with the steady-state distribution of the number of customers in that queue.…”