38 research outputs found
Simple and explicit bounds for multi-server queues with (and sometimes better) scaling
We consider the FCFS queue, and prove the first simple and explicit
bounds that scale as (and sometimes better). Here
denotes the corresponding traffic intensity. Conceptually, our results can be
viewed as a multi-server analogue of Kingman's bound. Our main results are
bounds for the tail of the steady-state queue length and the steady-state
probability of delay. The strength of our bounds (e.g. in the form of tail
decay rate) is a function of how many moments of the inter-arrival and service
distributions are assumed finite. More formally, suppose that the inter-arrival
and service times (distributed as random variables and respectively)
have finite th moment for some Let (respectively )
denote (respectively ). Then
our bounds (also for higher moments) are simple and explicit functions of
, and
only. Our bounds scale gracefully even when the number of
servers grows large and the traffic intensity converges to unity
simultaneously, as in the Halfin-Whitt scaling regime. Some of our bounds scale
better than in certain asymptotic regimes. More precisely,
they scale as multiplied by an inverse polynomial in These results formalize the intuition that bounds should be tighter
in light traffic as well as certain heavy-traffic regimes (e.g. with
fixed and large). In these same asymptotic regimes we also prove bounds for
the tail of the steady-state number in service.
Our main proofs proceed by explicitly analyzing the bounding process which
arises in the stochastic comparison bounds of amarnik and Goldberg for
multi-server queues. Along the way we derive several novel results for suprema
of random walks and pooled renewal processes which may be of independent
interest. We also prove several additional bounds using drift arguments (which
have much smaller pre-factors), and make several conjectures which would imply
further related bounds and generalizations
EUROPEAN CONFERENCE ON QUEUEING THEORY 2016
International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the TakĂĄcs Award for outstanding PhD thesis on "Queueing Theory and its Applications"
Scheduling for todayâs computer systems: bridging theory and practice
Scheduling is a fundamental technique for improving performance in computer systems. From web servers
to routers to operating systems, how the bottleneck device is scheduled has an enormous impact on the performance of the system as a whole. Given the immense literature studying scheduling, it is easy to think that we already understand enough about scheduling. But, modern computer system designs have highlighted a number of disconnects between traditional analytic results and the needs of system designers.
In particular, the idealized policies, metrics, and models used by analytic researchers do not match the policies, metrics, and scenarios that appear in real systems.
The goal of this thesis is to take a step towards modernizing the theory of scheduling in order to provide
results that apply to todayâs computer systems, and thus ease the burden on system designers. To accomplish
this goal, we provide new results that help to bridge each of the disconnects mentioned above. We will move beyond the study of idealized policies by introducing a new analytic framework where the focus is on scheduling heuristics and techniques rather than individual policies. By moving beyond the study of individual policies, our results apply to the complex hybrid policies that are often used in practice. For example, our results enable designers to understand how the policies that favor small job sizes are affected by the fact that real systems only have estimates of job sizes. In addition, we move beyond the study of mean response time
and provide results characterizing the distribution of response time and the fairness of scheduling policies.
These results allow us to understand how scheduling affects QoS guarantees and whether favoring small job sizes results in large job sizes being treated unfairly. Finally, we move beyond the simplified models traditionally used in scheduling research and provide results characterizing the effectiveness of scheduling in multiserver systems and when users are interactive. These results allow us to answer questions about the how to design multiserver systems and how to choose a workload generator when evaluating new scheduling designs
Recommended from our members
Exact Simulation Techniques in Applied Probability and Stochastic Optimization
This dissertation contains two parts. The first part introduces the first class of perfect sampling algorithms for the steady-state distribution of multi-server queues in which the arrival process is a general renewal process and the service times are independent and identically distributed (iid); the first-in-first-out FIFO GI/GI/c queue with 2 <= c < 1. Two main simulation algorithms are given in this context, where both of them are built on the classical dominated coupling from the past (DCFTP) protocol. In particular, the first algorithm uses a coupled multi-server vacation system as the upper bound process and it manages to simulate the vacation system backward in time from stationarity at time zero. The second algorithm utilizes the DCFTP protocol as well as the Random Assignment (RA) service discipline. Both algorithms have finite expected termination time with mild moment assumptions on the interarrival time and service time distributions. Our methods are also extended to produce exact simulation algorithms for Fork-Join queues and infinite server systems.
The second part presents general principles for the design and analysis of unbiased Monte Carlo estimators in a wide range of settings. The estimators possess finite work-normalized variance under mild regularity conditions. We apply the estimators to various applications including unbiased steady-state simulation of regenerative processes, unbiased optimization in Sample Average Approximations and distribution quantile estimation
Hybrid token-CDMA MAC protocol for wireless networks.
Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2009.Ad hoc networks are commonly known to implement IEEE 802.11 standard as their medium
access control (MAC) protocol. It is well known that token passing MAC schemes
outperform carrier-sense-multiple-access (CSMA) schemes, therefore, token passing MAC
protocols have gained popularity in recent years. In recent years, the research extends the
concept of token passing ' scheme to wireless settings since they have the potential of
achieving higher channel utilization than CSMA type schemes.
In this thesis, a hybrid Token-CDMA MAC protocol that is based on a token passing scheme
with the incorporation of code division multiple access (CDMA) is introduced. Using a
dynamic code distribution algorithm and a modified leaky-bucket policing system, the
hybrid protocol is able to provide both Quality of Service (QoS) and high network resource
utilization, while ensuring the stability of a network. This thesis begins with the introduction
of a new MAC protocol based on a token-passing strategy. The input traffic model used in
the simulation is a two-state Markov Modulated Poisson Process (MMPP). The data rate
QoS is enforced by implementing a modified leaky bucket mechanism in the proposed MAC
scheme. The simulation also takes into account channel link errors caused by the wireless
link by implementing a multi-layered Gilbert-Elliot model. The performance of the proposed
MAC scheme is examined by simulation, and compared to the performance of other MAC
protocols published in the literature. Simulation results demonstrate that the proposed hybrid
MAC scheme is effective in decreasing packet delay and significantly shortens the length of
the queue.
The thesis continues with the discussion of the analytical model for the hybrid Token CDMA
protocol. The proposed MAC scheme is analytically modelled as a multiserver
multiqueue (MSMQ) system with a gated service discipline. The analytical model is
categorized into three sections viz. the vacation model, the input model and the buffer model.
The throughput and delay performance are then computed and shown to closely match the
simulation results. Lastly, cross-layer optimization between the physical (PHY) and MAC
layers for the hybrid token-CDMA scheme is discussed. The proposed joint PHY -MAC
approach is based on the interaction between the two layers in order to enable the stations to
dynamically adjust the transmission parameters resulting in reduced mutual interference and
optimum system performance