1,985 research outputs found
The effect of service time variability on maximum queue lengths in M^X/G/1 queues
We study the impact of service-time distributions on the distribution of the
maximum queue length during a busy period for the M^X/G/1 queue. The maximum
queue length is an important random variable to understand when designing the
buffer size for finite buffer (M/G/1/n) systems. We show the somewhat
surprising result that for three variations of the preemptive LCFS discipline,
the maximum queue length during a busy period is smaller when service times are
more variable (in the convex sense).Comment: 12 page
Elastic calls in an integrated services network: the greater the call size variability the better the QoS
We study a telecommunications network integrating prioritized stream calls and delay tolerant elastic calls that are served with the remaining (varying) service capacity according to a processor sharing discipline. The remarkable observation is presented and analytically supported that the expected elastic call holding time is decreasing in the variability of the elastic call size distribution. As a consequence, network planning guidelines or admission control schemes that are developed based on deterministic or lightly variable elastic call sizes are likely to be conservative and inefficient, given the commonly acknowledged property of e.g.\ \textsc{www}\ documents to be heavy tailed. Application areas of the model and results include fixed \textsc{ip} or \textsc{atm} networks and mobile cellular \textsc{gsm}/\textsc{gprs} and \textsc{umts} networks. \u
Human activity modeling and Barabasi's queueing systems
It has been shown by A.-L. Barabasi that the priority based scheduling rules
in single stage queuing systems (QS) generates fat tail behavior for the tasks
waiting time distributions (WTD). Such fat tails are due to the waiting times
of very low priority tasks which stay unserved almost forever as the task
priority indices (PI) are "frozen in time" (i.e. a task priority is assigned
once for all to each incoming task). Relaxing the "frozen in time" assumption,
this paper studies the new dynamic behavior expected when the priority of each
incoming tasks is time-dependent (i.e. "aging mechanisms" are allowed). For two
class of models, namely 1) a population type model with an age structure and 2)
a QS with deadlines assigned to the incoming tasks which is operated under the
"earliest-deadline-first" policy, we are able to analytically extract some
relevant characteristics of the the tasks waiting time distribution. As the
aging mechanism ultimately assign high priority to any long waiting tasks, fat
tails in the WTD cannot find their origin in the scheduling rule alone thus
showing a fundamental difference between the present and the A.-L. Barabasi's
class of models.Comment: 16 pages, 2 figure
Revisiting Size-Based Scheduling with Estimated Job Sizes
We study size-based schedulers, and focus on the impact of inaccurate job
size information on response time and fairness. Our intent is to revisit
previous results, which allude to performance degradation for even small errors
on job size estimates, thus limiting the applicability of size-based
schedulers.
We show that scheduling performance is tightly connected to workload
characteristics: in the absence of large skew in the job size distribution,
even extremely imprecise estimates suffice to outperform size-oblivious
disciplines. Instead, when job sizes are heavily skewed, known size-based
disciplines suffer.
In this context, we show -- for the first time -- the dichotomy of
over-estimation versus under-estimation. The former is, in general, less
problematic than the latter, as its effects are localized to individual jobs.
Instead, under-estimation leads to severe problems that may affect a large
number of jobs.
We present an approach to mitigate these problems: our technique requires no
complex modifications to original scheduling policies and performs very well.
To support our claim, we proceed with a simulation-based evaluation that covers
an unprecedented large parameter space, which takes into account a variety of
synthetic and real workloads.
As a consequence, we show that size-based scheduling is practical and
outperforms alternatives in a wide array of use-cases, even in presence of
inaccurate size information.Comment: To be published in the proceedings of IEEE MASCOTS 201
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