Abstract: In this paper, the flow of different classes of patients
into a hospital is modelled and analyzed by using the queueing
network analyzer (QNA) algorithm and discrete event simulation.
Input data for QNA are the rate and variability parameters of the
arrival and service times in addition to the number of servers in each
facility. Patient flows mostly match real flow for a hospital in Egypt.
Based on the analysis of the waiting times, two approaches are
suggested for improving performance: Separating patients into
service groups, and adopting different service policies for sequencing
patients through hospital units. The separation of a specific group of
patients, with higher performance target, to be served separately from
the rest of patients requiring lower performance target, requires the
same capacity while improves performance for the selected group of
patients with higher target. Besides, it is shown that adopting the
shortest processing time and shortest remaining processing time
service policies among other tested policies would results in,
respectively, 11.47% and 13.75% reduction in average waiting time
relative to first come first served policy.
Abstract: We study four models of a three server queueing system with Bernoulli schedule optional server vacations. Customers arriving at the system one by one in a Poisson process are provided identical exponential service by three parallel servers according to a first-come, first served queue discipline. In model A, all three servers may be allowed a vacation at one time, in Model B at the most two of the three servers may be allowed a vacation at one time, in model C at the most one server is allowed a vacation, and in model D no server is allowed a vacation. We study steady the state behavior of the four models and obtain steady state probability generating functions for the queue size at a random point of time for all states of the system. In model D, a known result for a three server queueing system without server vacations is derived.
Abstract: This paper studies a random fuzzy queueing system
that the interarrival times of customers arriving at the server and
the service times are independent and identically distributed random
fuzzy variables. We match the random fuzzy queueing system with
the random fuzzy alternating renewal process and we do not use from
α-pessimistic and α-optimistic values to estimate the average chance
of the event ”random fuzzy queueing system is busy at time t”, we
employ the fuzzy simulation method in practical applications. Some
theorem is proved and finally we solve a numerical example with
fuzzy simulation method.
Abstract: This paper presents a finite buffer renewal input single working vacation and vacation interruption queue with state dependent services and state dependent vacations, which has a wide range of applications in several areas including manufacturing, wireless communication systems. Service times during busy period, vacation period and vacation times are exponentially distributed and are state dependent. As a result of the finite waiting space, state dependent services and state dependent vacation policies, the analysis of these queueing models needs special attention. We provide a recursive method using the supplementary variable technique to compute the stationary queue length distributions at pre-arrival and arbitrary epochs. An efficient computational algorithm of the model is presented which is fast and accurate and easy to implement. Various performance measures have been discussed. Finally, some special cases and numerical results have been depicted in the form of tables and graphs.
Abstract: In this paper, we study statistical multiplexing of VBR
video in ATM networks. ATM promises to provide high speed realtime
multi-point to central video transmission for telemedicine
applications in rural hospitals and in emergency medical services.
Video coders are known to produce variable bit rate (VBR) signals
and the effects of aggregating these VBR signals need to be
determined in order to design a telemedicine network infrastructure
capable of carrying these signals. We first model the VBR video
signal and simulate it using a generic continuous-data autoregressive
(AR) scheme. We carry out the queueing analysis by the Fluid
Approximation Model (FAM) and the Markov Modulated Poisson
Process (MMPP). The study has shown a trade off: multiplexing
VBR signals reduces burstiness and improves resource utilization,
however, the buffer size needs to be increased with an associated
economic cost. We also show that the MMPP model and the Fluid
Approximation model fit best, respectively, the cell region and the
burst region. Therefore, a hybrid MMPP and FAM completely
characterizes the overall performance of the ATM statistical
multiplexer. The ramifications of this technology are clear: speed,
reliability (lower loss rate and jitter), and increased capacity in video
transmission for telemedicine. With migration to full IP-based
networks still a long way to achieving both high speed and high
quality of service, the proposed ATM architecture will remain of
significant use for telemedicine.
Abstract: Traditionally, Internet has provided best-effort service to every user regardless of its requirements. However, as Internet becomes universally available, users demand more bandwidth and applications require more and more resources, and interest has developed in having the Internet provide some degree of Quality of Service. Although QoS is an important issue, the question of how it will be brought into the Internet has not been solved yet. Researches, due to the rapid advances in technology are proposing new and more desirable capabilities for the next generation of IP infrastructures. But neither all applications demand the same amount of resources, nor all users are service providers. In this way, this paper is the first of a series of papers that presents an architecture as a first step to the optimization of QoS in the Internet environment as a solution to a SMSE's problem whose objective is to provide public service to internet with certain Quality of Service expectations. The service provides new business opportunities, but also presents new challenges. We have designed and implemented a scalable service framework that supports adaptive bandwidth based on user demands, and the billing based on usage and on QoS. The developed application has been evaluated and the results show that traffic limiting works at optimum and so it does exceeding bandwidth distribution. However, some considerations are done and currently research is under way in two basic areas: (i) development and testing new transfer protocols, and (ii) developing new strategies for traffic improvements based on service differentiation.
Abstract: This paper proposes a bi-objective model for the
facility location problem under a congestion system. The idea of the
model is motivated by applications of locating servers in bank
automated teller machines (ATMS), communication networks, and so
on. This model can be specifically considered for situations in which
fixed service facilities are congested by stochastic demand within
queueing framework. We formulate this model with two perspectives
simultaneously: (i) customers and (ii) service provider. The
objectives of the model are to minimize (i) the total expected
travelling and waiting time and (ii) the average facility idle-time.
This model represents a mixed-integer nonlinear programming
problem which belongs to the class of NP-hard problems. In addition,
to solve the model, two metaheuristic algorithms including nondominated
sorting genetic algorithms (NSGA-II) and non-dominated
ranking genetic algorithms (NRGA) are proposed. Besides, to
evaluate the performance of the two algorithms some numerical
examples are produced and analyzed with some metrics to determine
which algorithm works better.
Abstract: This paper treats a discrete-time batch arrival queue with single working vacation. The main purpose of this paper is to present a performance analysis of this system by using the supplementary variable technique. For this purpose, we first analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. Next, we present the stationary distributions of the system length as well as some performance measures at random epochs by using the supplementary variable method. Thirdly, still based on the supplementary variable method we give the probability generating function (PGF) of the number of customers at the beginning of a busy period and give a stochastic decomposition formulae for the PGF of the stationary system length at the departure epochs. Additionally, we investigate the relation between our discretetime system and its continuous counterpart. Finally, some numerical examples show the influence of the parameters on some crucial performance characteristics of the system.
Abstract: In communication networks where communication nodes are connected with finite capacity transmission links, the packet inter-arrival times are strongly correlated with the packet length and the link capacity (or the packet service time). Such correlation affects the system performance significantly, but little attention has been paid to this issue. In this paper, we propose a mathematical framework to study the impact of the correlation between the packet service times and the packet inter-arrival times on system performance. With our mathematical model, we analyze the system performance, e.g., the unfinished work of the system, and show that the correlation affects the system performance significantly. Some numerical examples are also provided.
Abstract: We present a new numerical method for the computation of the steady-state solution of Markov chains. Theoretical analyses show that the proposed method, with a contraction factor α, converges to the one-dimensional null space of singular linear systems of the form Ax = 0. Numerical experiments are used to illustrate the effectiveness of the proposed method, with applications to a class of interesting models in the domain of tandem queueing networks.
Abstract: In this work, we study the impact of dynamically
changing link slowdowns on the stability properties of packetswitched
networks under the Adversarial Queueing Theory
framework. Especially, we consider the Adversarial, Quasi-Static
Slowdown Queueing Theory model, where each link slowdown may
take on values in the two-valued set of integers {1, D} with D > 1
which remain fixed for a long time, under a (w, ¤ü)-adversary. In this
framework, we present an innovative systematic construction for the
estimation of adversarial injection rate lower bounds, which, if
exceeded, cause instability in networks that use the LIS (Longest-in-
System) protocol for contention-resolution. In addition, we show that
a network that uses the LIS protocol for contention-resolution may
result in dropping its instability bound at injection rates ¤ü > 0 when
the network size and the high slowdown D take large values. This is
the best ever known instability lower bound for LIS networks.
Abstract: The modern queueing theory is one of the powerful
tools for a quantitative and qualitative analysis of communication systems, computer networks, transportation systems, and many other technical systems. The paper is designated to the analysis of queueing
systems, arising in the networks theory and communications theory
(called open queueing network). The authors of this research in the
sphere of queueing theory present the theorem about the law of the iterated logarithm (LIL) for the queue length of a customers in open
queueing network and its application to the mathematical model of
the open message switching system.
Abstract: In the queueing theory, it is assumed that customer
arrivals correspond to a Poisson process and service time has the
exponential distribution. Using these assumptions, the behaviour of
the queueing system can be described by means of Markov chains
and it is possible to derive the characteristics of the system. In the
paper, these theoretical approaches are presented on several types of
systems and it is also shown how to compute the characteristics in a
situation when these assumptions are not satisfied
Abstract: In this work, we study the impact of dynamically changing link slowdowns on the stability properties of packetswitched networks under the Adversarial Queueing Theory framework. Especially, we consider the Adversarial, Quasi-Static Slowdown Queueing Theory model, where each link slowdown may take on values in the two-valued set of integers {1, D} with D > 1 which remain fixed for a long time, under a (w, p)-adversary. In this framework, we present an innovative systematic construction for the estimation of adversarial injection rate lower bounds, which, if exceeded, cause instability in networks that use the LIS (Longest-in- System) protocol for contention-resolution. In addition, we show that a network that uses the LIS protocol for contention-resolution may result in dropping its instability bound at injection rates p > 0 when the network size and the high slowdown D take large values. This is the best ever known instability lower bound for LIS networks.
Abstract: Video sensor networks operate on stringent requirements
of latency. Packets have a deadline within which they have
to be delivered. Violation of the deadline causes a packet to be
treated as lost and the loss of packets ultimately affects the quality
of the application. Network latency is typically a function of many
interacting components. In this paper, we propose ways of reducing
the forwarding latency of a packet at intermediate nodes. The
forwarding latency is caused by a combination of processing delay
and queueing delay. The former is incurred in order to determine the
next hop in dynamic routing. We show that unless link failures in a
very specific and unlikely pattern, a vast majority of these lookups
are redundant. To counter this we propose source routing as the
routing strategy. However, source routing suffers from issues related
to scalability and being impervious to network dynamics. We propose
solutions to counter these and show that source routing is definitely
a viable option in practical sized video networks. We also propose a
fast and fair packet scheduling algorithm that reduces queueing delay
at the nodes. We support our claims through extensive simulation on
realistic topologies with practical traffic loads and failure patterns.
Abstract: In the present communication, we have studied
different variations in the entropy measures in the different states of
queueing processes. In case of steady state queuing process, it has
been shown that as the arrival rate increases, the uncertainty
increases whereas in the case of non-steady birth-death process, it is
shown that the uncertainty varies differently. In this pattern, it first
increases and attains its maximum value and then with the passage of
time, it decreases and attains its minimum value.
Abstract: Urban road network traffic has become one of the
most studied research topics in the last decades. This is mainly due to
the enlargement of the cities and the growing number of motor
vehicles traveling in this road network. One of the most sensitive
problems is to verify if the network is congestion-free. Another
related problem is the automatic reconfiguration of the network
without building new roads to alleviate congestions. These problems
require an accurate model of the traffic to determine the steady state
of the system. An alternative is to simulate the traffic to see if there
are congestions and when and where they occur. One key issue is to
find an adequate model for road intersections. Once the model
established, either a large scale model is built or the intersection is
represented by its performance measures and simulation for analysis.
In both cases, it is important to seek the queueing model to represent
the road intersection. In this paper, we propose to model the road
intersection as a BCMP queueing network and we compare this
analytical model against a simulation model for validation.