Approximate Analysis of Fork/Join Synchronization in Parallel Queues
IEEE Transactions on Computers
Asymptotic expansions for waiting time probabilities in an M/G/1 queue with long-tailed service time
Queueing Systems: Theory and Applications
A practical guide to heavy tails
Asymptotics for M/G/1 low-priority waiting-time tail probabilities
Queueing Systems: Theory and Applications
Asymptotics of stochastic networks with subexponential service times
Queueing Systems: Theory and Applications
Operations Research
Asymptotics of stochastic networks with subexponential service times
Queueing Systems: Theory and Applications
Non-asymptotic delay bounds for networks with heavy-tailed traffic
INFOCOM'10 Proceedings of the 29th conference on Information communications
Tandem queues with subexponential service times and finite buffers
Queueing Systems: Theory and Applications
| Hi-index | 0.00 |
Consider a stable FIFO GI/GI/1\,\rightarrow\,/GI/1 tandem queue in which the equilibrium distribution of service time at the second node S(2) is subexponential. It is shown that when the service time at the first node has a lighter tail, the tail of steady-state delay at the second node, D(2), has the same asymptotics as if it were a GI/GI/1 queue: P(D(2) x) \sim {{\rho_2} \over {1-\rho_2}}P(S_{\mathrm{e}}(2) x), \quad x{\rightarrow}{\infty}, where S_{\mathrm{e}}(2) has equilibrium (integrated tail) density P(S(2) x)/ {E[S(2)]}, and \rho_2 = \lambda {E[S(2)]} (\lambda is the arrival rate of customers). The same result holds for tandem queues with more than two stations. For split-match (fork-join) queues with subexponential service times, we derive the asymptotics for both the sojourn time and the queue length. Finally, more generally, we consider feedforward generalized Jackson networks and obtain similar results.