118,886 research outputs found
Approximations and Bounds for (n, k) Fork-Join Queues: A Linear Transformation Approach
Compared to basic fork-join queues, a job in (n, k) fork-join queues only
needs its k out of all n sub-tasks to be finished. Since (n, k) fork-join
queues are prevalent in popular distributed systems, erasure coding based cloud
storages, and modern network protocols like multipath routing, estimating the
sojourn time of such queues is thus critical for the performance measurement
and resource plan of computer clusters. However, the estimating keeps to be a
well-known open challenge for years, and only rough bounds for a limited range
of load factors have been given. In this paper, we developed a closed-form
linear transformation technique for jointly-identical random variables: An
order statistic can be represented by a linear combination of maxima. This
brand-new technique is then used to transform the sojourn time of non-purging
(n, k) fork-join queues into a linear combination of the sojourn times of basic
(k, k), (k+1, k+1), ..., (n, n) fork-join queues. Consequently, existing
approximations for basic fork-join queues can be bridged to the approximations
for non-purging (n, k) fork-join queues. The uncovered approximations are then
used to improve the upper bounds for purging (n, k) fork-join queues.
Simulation experiments show that this linear transformation approach is
practiced well for moderate n and relatively large k.Comment: 10 page
Concurrent Channel Probing and Data Transmission in Full-duplex MIMO Systems
An essential step for achieving multiplexing gain in MIMO downlink systems is
to collect accurate channel state information (CSI) from the users.
Traditionally, CSIs have to be collected before any data can be transmitted.
Such a sequential scheme incurs a large feedback overhead, which substantially
limits the multiplexing gain especially in a network with a large number of
users. In this paper, we propose a novel approach to mitigate the feedback
overhead by leveraging the recently developed Full-duplex radios. Our approach
is based on the key observation that using Full-duplex radios, when the
base-station (BS) is collecting CSI of one user through the uplink channel, it
can use the downlink channel to simultaneously transmit data to other
(non-interfering) users for which CSIs are already known. By allowing
concurrent channel probing and data transmission, our scheme can potentially
achieve a higher throughput compared to traditional schemes using Half-duplex
radios. The new flexibility introduced by our scheme, however, also leads to
fundamental challenges in achieving throughout optimal scheduling. In this
paper, we make an initial effort to this important problem by considering a
simplified group interference model. We develop a throughput optimal scheduling
policy with complexity , where is the number of users and
is the number of user groups. To further reduce the complexity, we propose a
greedy policy with complexity that not only achieves at least 2/3
of the optimal throughput region, but also outperforms any feasible Half-duplex
solutions. We derive the throughput gain offered by Full-duplex under different
system parameters and show the advantage of our algorithms through numerical
studies.Comment: Technical repor
The Mx/G/1 queue with queue length dependent service times
We deal with the MX/G/1 queue where service times depend on the queue length at the service initiation. By using Markov renewal theory, we derive the queue length distribution at departure epochs. We also obtain the transient queue length distribution at time t and its limiting distribution and the virtual waiting time distribution. The numerical results for transient mean queue length and queue length distributions are given.Bong Dae Choi, Yeong Cheol Kim, Yang Woo Shin, and Charles E. M. Pearc
Finding Simple Shortest Paths and Cycles
The problem of finding multiple simple shortest paths in a weighted directed
graph has many applications, and is considerably more difficult than
the corresponding problem when cycles are allowed in the paths. Even for a
single source-sink pair, it is known that two simple shortest paths cannot be
found in time polynomially smaller than (where ) unless the
All-Pairs Shortest Paths problem can be solved in a similar time bound. The
latter is a well-known open problem in algorithm design. We consider the
all-pairs version of the problem, and we give a new algorithm to find
simple shortest paths for all pairs of vertices. For , our algorithm runs
in time (where ), which is almost the same bound as
for the single pair case, and for we improve earlier bounds. Our approach
is based on forming suitable path extensions to find simple shortest paths;
this method is different from the `detour finding' technique used in most of
the prior work on simple shortest paths, replacement paths, and distance
sensitivity oracles.
Enumerating simple cycles is a well-studied classical problem. We present new
algorithms for generating simple cycles and simple paths in in
non-decreasing order of their weights; the algorithm for generating simple
paths is much faster, and uses another variant of path extensions. We also give
hardness results for sparse graphs, relative to the complexity of computing a
minimum weight cycle in a graph, for several variants of problems related to
finding simple paths and cycles.Comment: The current version includes new results for undirected graphs. In
Section 4, the notion of an (m,n) reduction is generalized to an f(m,n)
reductio
Power series approximations for two-class generalized processor sharing systems
We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If both queues are nonempty, a customer of queue 1 is served with probability beta, and a customer of queue 2 is served with probability 1-beta. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating function U(z (1),z (2)) of the stationary queue lengths in terms of a functional equation, and show how to solve this using the theory of boundary value problems. Then, we propose to use the same functional equation to obtain a power series for U(z (1),z (2)) in beta. The first coefficient of this power series corresponds to the priority case beta=0, which allows for an explicit solution. All higher coefficients are expressed in terms of the priority case. Accurate approximations for the mean stationary queue lengths are obtained from combining truncated power series and Pad, approximation
Stability Analysis of GI/G/c/K Retrial Queue with Constant Retrial Rate
We consider a GI/G/c/K-type retrial queueing system with constant retrial
rate. The system consists of a primary queue and an orbit queue. The primary
queue has identical servers and can accommodate the maximal number of
jobs. If a newly arriving job finds the full primary queue, it joins the orbit.
The original primary jobs arrive to the system according to a renewal process.
The jobs have general i.i.d. service times. A job in front of the orbit queue
retries to enter the primary queue after an exponentially distributed time
independent of the orbit queue length. Telephone exchange systems, Medium
Access Protocols and short TCP transfers are just some applications of the
proposed queueing system. For this system we establish minimal sufficient
stability conditions. Our model is very general. In addition, to the known
particular cases (e.g., M/G/1/1 or M/M/c/c systems), the proposed model covers
as particular cases the deterministic service model and the Erlang model with
constant retrial rate. The latter particular cases have not been considered in
the past. The obtained stability conditions have clear probabilistic
interpretation
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Survey of unified approaches to integrated-service networks
The increasing demand for communication services, coupled with recent technological advances in communication media and switching techniques, has resulted in a proliferation of new and expanded services. Currently, networks are needed which can transmit voice, data, and video services in an application-independent fashion. Unified approaches employ a single switching technique across the entire network bandwidth, thus, allowing services to be switched in an application-independent manner. This paper presents a taxonomy of integrated-service networks including a look at N-ISDN, while focusing on unified approaches to integrated-service networks.The two most promising unified approaches are burst and fast packet switching. Burst switching is a circuit switching-based approach which allocates channel bandwidth to a connection only during the transmission of "bursts" of information. Fast packet switching is a packet switching-based approach which can be characterized by very high transmission rates on network links and simple, hardwired protocols which match the rapid channel speed of the network. Both approaches are being proposed as possible implementations for integrated-service networks. We survey these two approaches, and also examine the key performance issues found in fast packet switching. We then present the results of a simulation study of a fast packet switching network
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