769 research outputs found
Sprinklers: A Randomized Variable-Size Striping Approach to Reordering-Free Load-Balanced Switching
Internet traffic continues to grow exponentially, calling for switches that
can scale well in both size and speed. While load-balanced switches can achieve
such scalability, they suffer from a fundamental packet reordering problem.
Existing proposals either suffer from poor worst-case packet delays or require
sophisticated matching mechanisms. In this paper, we propose a new family of
stable load-balanced switches called "Sprinklers" that has comparable
implementation cost and performance as the baseline load-balanced switch, but
yet can guarantee packet ordering. The main idea is to force all packets within
the same virtual output queue (VOQ) to traverse the same "fat path" through the
switch, so that packet reordering cannot occur. At the core of Sprinklers are
two key innovations: a randomized way to determine the "fat path" for each VOQ,
and a way to determine its "fatness" roughly in proportion to the rate of the
VOQ. These innovations enable Sprinklers to achieve near-perfect load-balancing
under arbitrary admissible traffic. Proving this property rigorously using
novel worst-case large deviation techniques is another key contribution of this
work
Restricted Mobility Improves Delay-Throughput Trade-offs in Mobile Ad-Hoc Networks
In this paper we revisit two classes of mobility models which are widely used to repre-sent users ’ mobility in wireless networks: Random Waypoint (RWP) and Random Direction (RD). For both models we obtain systems of partial differential equations which describe the evolution of the users ’ distribution. For the RD model, we show how the equations can be solved analytically both in the stationary and transient regime adopting standard mathematical techniques. Our main contributions are i) simple expressions which relate the transient dura-tion to the model parameters; ii) the definition of a generalized random direction model whose stationary distribution of mobiles in the physical space corresponds to an assigned distribution
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
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
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