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Analysis of a discrete-time single-server queue with bursty imputs for traffic control in ATM networks
Due to a large number of bursty traffic sources that an ATM network is expected to support, controlling network traffic becomes essential to provide a desirable level of network performance with its users. Admission control and traffic smoothing are among the most promising control techniques for an ATM network. To evaluate the performance of an ATM network when it is subject to admission control or traffic smoothing, we build a discrete-time single-server queueing model where a new call joins the existing calls.In our model. it is assumed that the cell arrivals from a new call follow a general distribution. It is also assumed that the aggregated arrivals of cells from the existing calls form batch arrivals with a general distribution for the batch size and a geometric distribution for the interarrival times of batches. We consider both finite and infinite buffer cases, and analytically obtain the waiting time distribution and cell loss probability for a new call and for existing calls. Our analysis is an exact one. Through numerical examples, we investigate how the network performance depends on the statistics of a new call (burstiness, time that a call stays in active or inactive state, etc.). We also demonstrate the effectiveness of traffic smoothing to reduce network congestion
Multi-type TASEP in discrete time
The TASEP (totally asymmetric simple exclusion process) is a basic model for
an one-dimensional interacting particle system with non-reversible dynamics.
Despite the simplicity of the model it shows a very rich and interesting
behaviour. In this paper we study some aspects of the TASEP in discrete time
and compare the results to the recently obtained results for the TASEP in
continuous time. In particular we focus on stationary distributions for
multi-type models, speeds of second-class particles, collision probabilities
and the "speed process". In discrete time, jump attempts may occur at different
sites simultaneously, and the order in which these attempts are processed is
important; we consider various natural update rules.Comment: 36 page
Channel-Aware Random Access in the Presence of Channel Estimation Errors
In this work, we consider the random access of nodes adapting their
transmission probability based on the local channel state information (CSI) in
a decentralized manner, which is called CARA. The CSI is not directly available
to each node but estimated with some errors in our scenario. Thus, the impact
of imperfect CSI on the performance of CARA is our main concern. Specifically,
an exact stability analysis is carried out when a pair of bursty sources are
competing for a common receiver and, thereby, have interdependent services. The
analysis also takes into account the compound effects of the multipacket
reception (MPR) capability at the receiver. The contributions in this paper are
twofold: first, we obtain the exact stability region of CARA in the presence of
channel estimation errors; such an assessment is necessary as the errors in
channel estimation are inevitable in the practical situation. Secondly, we
compare the performance of CARA to that achieved by the class of stationary
scheduling policies that make decisions in a centralized manner based on the
CSI feedback. It is shown that the stability region of CARA is not necessarily
a subset of that of centralized schedulers as the MPR capability improves.Comment: The material in this paper was presented in part at the IEEE
International Symposium on Information Theory, Cambridge, MA, USA, July 201
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
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