8,202 research outputs found
Understanding CHOKe: throughput and spatial characteristics
A recently proposed active queue management, CHOKe, is stateless, simple to implement, yet surprisingly effective in protecting TCP from UDP flows. We present an equilibrium model of TCP/CHOKe. We prove that, provided the number of TCP flows is large, the UDP bandwidth share peaks at (e+1)/sup -1/=0.269 when UDP input rate is slightly larger than link capacity, and drops to zero as UDP input rate tends to infinity. We clarify the spatial characteristics of the leaky buffer under CHOKe that produce this throughput behavior. Specifically, we prove that, as UDP input rate increases, even though the total number of UDP packets in the queue increases, their spatial distribution becomes more and more concentrated near the tail of the queue, and drops rapidly to zero toward the head of the queue. In stark contrast to a nonleaky FIFO buffer where UDP bandwidth shares would approach 1 as its input rate increases without bound, under CHOKe, UDP simultaneously maintains a large number of packets in the queue and receives a vanishingly small bandwidth share, the mechanism through which CHOKe protects TCP flows
Asymptotic behavior of the loss probability for an M/G/1/N queue with vacations
In this paper, asymptotic properties of the loss probability are considered
for an M/G/1/N queue with server vacations and exhaustive service discipline,
denoted by an M/G/1/N -(V, E)-queue. Exact asymptotic rates of the loss
probability are obtained for the cases in which the traffic intensity is
smaller than, equal to and greater than one, respectively. When the vacation
time is zero, the model considered degenerates to the standard M/G/1/N queue.
For this standard queueing model, our analysis provides new or extended
asymptotic results for the loss probability. In terms of the duality
relationship between the M/G/1/N and GI/M/1/N queues, we also provide
asymptotic properties for the standard GI/M/1/N model
A sufficient condition for the subexponential asymptotics of GI/G/1-type Markov chains with queueing applications
The main contribution of this paper is to present a new sufficient condition
for the subexponential asymptotics of the stationary distribution of a
GI/GI/1-type Markov chain without jumps from level "infinity" to level zero.
For simplicity, we call such Markov chains {\it GI/GI/1-type Markov chains
without disasters} because they are often used to analyze semi-Markovian queues
without "disasters", which are negative customers who remove all the customers
in the system (including themselves) on their arrivals. In this paper, we
demonstrate the application of our main result to the stationary queue length
distribution in the standard BMAP/GI/1 queue. Thus we obtain new asymptotic
formulas and prove the existing formulas under weaker conditions than those in
the literature. In addition, applying our main result to a single-server queue
with Markovian arrivals and the -bulk-service rule (i.e., MAP//1 queue), we obatin a subexponential asymptotic formula for the
stationary queue length distribution.Comment: Submitted for revie
Stationary Distribution Convergence of the Offered Waiting Processes for GI/GI/1+GI Queues in Heavy Traffic
A result of Ward and Glynn (2005) asserts that the sequence of scaled offered
waiting time processes of the queue converges weakly to a
reflected Ornstein-Uhlenbeck process (ROU) in the positive real line, as the
traffic intensity approaches one. As a consequence, the stationary distribution
of a ROU process, which is a truncated normal, should approximate the scaled
stationary distribution of the offered waiting time in a queue;
however, no such result has been proved. We prove the aforementioned
convergence, and the convergence of the moments, in heavy traffic, thus
resolving a question left open in Ward and Glynn (2005). In comparison to
Kingman's classical result in Kingman (1961) showing that an exponential
distribution approximates the scaled stationary offered waiting time
distribution in a queue in heavy traffic, our result confirms that
the addition of customer abandonment has a non-trivial effect on the queue
stationary behavior.Comment: 29 page
On the maximum queue length in the supermarket model
There are queues, each with a single server. Customers arrive in a
Poisson process at rate , where . Upon arrival each
customer selects servers uniformly at random, and joins the queue at a
least-loaded server among those chosen. Service times are independent
exponentially distributed random variables with mean 1. We show that the system
is rapidly mixing, and then investigate the maximum length of a queue in the
equilibrium distribution. We prove that with probability tending to 1 as
the maximum queue length takes at most two values, which are
.Comment: Published at http://dx.doi.org/10.1214/00911790500000710 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Stationary analysis of a single queue with remaining service time dependent arrivals
We study a generalization of the system (denoted by ) with
independent and identically distributed (iid) service times and with an arrival
process whose arrival rate depends on the remaining service
time of the current customer being served. We derive a natural stability
condition and provide a stationary analysis under it both at service completion
times (of the queue length process) and in continuous time (of the queue length
and the residual service time). In particular, we show that the stationary
measure of queue length at service completion times is equal to that of a
corresponding system. For we show that the continuous time
stationary measure of the system is linked to the system via a
time change. As opposed to the queue, the stationary measure of queue
length of the system at service completions differs from its marginal
distribution under the continuous time stationary measure. Thus, in general,
arrivals of the system do not see time averages. We derive formulas
for the average queue length, probability of an empty system and average
waiting time under the continuous time stationary measure. We provide examples
showing the effect of changing the reshaping function on the average waiting
time.Comment: 31 pages, 3 Figure
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