Heavy Tails in Multi-Server Queue

Heavy Tails in Multi-Server Queue

In this paper, the asymptotic behaviour of the distribution tail of the stationary waiting time W in the GI/GI/2 FCFS queue is studied. Under subexponential-type assumptions on the service time distribution, bounds and sharp asymptotics are given for the probability P{W > x}. We also get asymptotics for the distribution tail of a stationary two-dimensional workload vector and of a stationary qu...

Heavy Tails in Multi-Server Queue1

In this paper, the asymptotic behaviour of the distribution tail of the stationary waiting time W in the GI/GI/2 FCFS queue is studied. Under subexponential-type assumptions on the service time distribution, bounds and sharp asymptotics are given for the probability P{W > x}. We also get asymptotics for the distribution tail of a stationary two-dimensional workload vector and of a stationary qu...

On Large Delays in Multi-Server Queues with Heavy Tails

We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s FCFS queue. These bounds depend on the value of the traffic load ρ which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a “principl...

Sojourn time tails in the single server queue with heavy-tailed service times

We consider the GI/GI/1 queue with regularly varying service requirement distribution of index −α. It is well known that, in the M/G/1 FCFS queue, the sojourn time distribution is also regularly varying, of index 1 − α, whereas in the case of LCFS or Processor Sharing, the sojourn time distribution is regularly varying of index −α. That raises the question whether there exist service discipline...

Controllable Multi-Server Queue with Balking (TECHNICAL NOTE)