• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.389-405
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• 1995

Output processes emanating from exit arcs in a mulitple server open Jackson network with node i having $s_i$ servers are determined. Beutler and Melamed (1978) showed, for traffics on all exit arcs of single server open Jackson network in equilibrium, that the customer streams leaving any exit set are Poisson and that the collections over all nodes which yield the Poisson departure processes are mutually independent. In this paper we generalize the above results to multiple servers open Jackson network in equilibrium. While no weak limit result is possible under the equilibrium condition, nonetheless approximations to the distributions of maximum queue lengths for no feedback nodes in multiple servers open Jackson network are established.

• Journal of the Korean Statistical Society
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• v.32 no.4
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• pp.359-371
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• 2003

We consider the probability that the total population of a stable Jackson network reaches a given large value. By using the fluid limit of the reversed network, we derive new upper and lower bounds on this probability, which are sharper than those in Glasserman and Kou (1995). In particular, the improved lower bound is useful for analyzing the performance of an importance sampling estimator for the overflow probability in Jackson tandem networks. Bounds on the expected time to overflow are also obtained.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.109-113
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• 2000

We consider the probability that the total population of a Jackson network exceeds a given large value. By using the relation to the stationary distribution, we derive upper and lower bounds on this probability. These bounds imply the stronger logarithmic limit than that in Glasserman and Kou(1995) when several nodes have the same maximal load.

• Korean Management Science Review
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• v.27 no.1
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• pp.17-31
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• 2010

Patients entering an emergency care center in a hospital usually visit medical processes in different orders depending on the urgency level and the medical treatments required. We formulate the patient flows among diverse processes in an emergency care center using the Jackson network, which is one of the queueing networks, in order to evaluate the system performances such as the expected queue length and the expected waiting time. We present a case study based on actual data collected from an emergency care center in a hospital, in order to prove the validity of applying the Jackson network model in practice. After assessing the current system performances, we provide operational strategies to reduce waiting at the bottleneck processes and evaluate the impact of those strategies on the entire system.

• ETRI Journal
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• v.24 no.5
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• pp.381-390
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• 2002

We analyze the performance of a telecommunications management network (TMN) system using models of networks of queues, Jackson's theorem, and simulation. TMN systems for managing public asynchronous transfer mode (ATM) networks generally have a four-level hierarchical structure consisting of a network management system, a few element management systems (EMSs), and several pairs of agents and ATM switches. We construct a Jackson's queuing network and present formulae to calculate its performance measures: distributions of queue lengths and waiting times, mean message response time, and maximum throughput. We perform a numerical analysis and a simulation analysis and compare the results.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.225-232
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• 2005

We obtain the approximation order to a smooth function on a compact subset of $\mathbb{R}$ by generalized translation networks. In our study, the activation function is infinitely many times continuously differentiable function but it does not have special properties around ${\infty}$ and $-{\infty}$ like a sigmoidal activation function. Using the Jackson's Theorem, we get the approximation order. Especially, we obtain the approximation order by a neural network with a fixed threshold.

• ETRI Journal
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• v.25 no.1
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• pp.34-40
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• 2003

This paper considers a TMN-based management system for the management of public ATM switching networks using a four-level hierarchical structure consisting of one network management system, several element management systems, and several agent-ATM switch pairs. Using Jackson's queuing model, we analyze the effects of one TMN command on the performance of the component ATM switch in processing local calls. The TMN command considered is the permanent virtual call connection. We analyze four performance measures of ATM switches- utilization, mean queue length and mean waiting time for the processor directly interfacing with the subscriber lines and trunks, and the call setup delay of the ATM switch- and compare the results with those from Jackson's queuing model.

• Proceedings of the Korea Information Processing Society Conference
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• 2001.10b
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• pp.1533-1536
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• 2001

This paper considers the TMN system for management of public ATM switching network which has the four-level hierarchical structure consisting of one network management system, a few element management system and several agent-ATM switch pairs, respectively. The effects of one TMN command on the local call processing performance of the component ATM switch an analyzed using Jackson's queueing model. The TMN command considered is the permanent virtual call connection, and the performance measures of ATM switch are the utilization, mean queue length and mean waiting time for the processor interfacing the subscriber lines and trunks directly, and the call setup delay of the ATM switch.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.4
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• pp.15-23
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• 1995

In this paper, we evaluate the performance of a transient queueing approximation when it is applied to modeling computer communication networks. An operational computer network that uses the ISO IS-IS(Intermediate System-Intermediate System) routing protocol is modeled as a Jackson network. The primary goal of the approximation pursued in the study was to provide transient queue statistics comparable in accuracy to the results from conventional Monte Carlo simulations. A closure approximation of the M/M/1 queueing system was extended to the general Jackson network in order to obtain transient queue statistics. The performance of the approximation was compared to a discrete event simulation under nonstationary conditions. The transient results from the two simulations are compared on the basis of queue size and computer execution time. Under nonstationary conditions, the approximations for the mean and variance of the number of packets in the queue erer fairly close to the simulation values. The approximation offered substantial speed improvements over the discrete event simulation. The closure approximation provided a good alternative Monte Carlo simulation of the computer networks.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.1035-1045
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• 2001

We present two decomposition approximations for the mean sojourn times in open single class queing networks. If there is a single bottleneck station, the approximations are asymptotically exact in both light and heavy traffic. When applied to a Jackson network or an M/G/1 queue, these approximations are exact for all values of the traffic intensity.