# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

All Issues

## Journal of Industrial & Management Optimization

July 2009 , Volume 5 , Issue 3

Special Issue for the Third Asia-Pacific Symposium
on Queueing Theory and Network Applications (QTNA2008)
Guest Editors: Wuyi Yue, Yutaka Takahashi and Hideaki Takagi

Special Issue Papers: 417-567; Regular Papers: 569-682

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2009, 5(3): i-iii doi: 10.3934/jimo.2009.5.3i +[Abstract](1270) +[PDF](41.5KB)
Abstract:
This special issue is a collection of papers selected from the revised and expanded versions of papers presented at the Third Asia-Pacific Symposium on Queueing Theory and Network Applications (QTNA2008), July 30-August 2, 2008, Taipei, Taiwan.
Included are 10 papers of high quality which were selected from among those contributed papers in QTNA2008. They have all been peer-reviewed by two or more referees according to the normal standard of the journal.
The special issue aims at publishing high quality papers dealing with performance analysis and system management of communication networks and related systems.

For more information please click the “Full Text” above.
2009, 5(3): 417-430 doi: 10.3934/jimo.2009.5.417 +[Abstract](1599) +[PDF](171.1KB)
Abstract:
In this paper, we present analysis for an M/M/R/N queueing system with balking, reneging and server breakdowns. The server is subject to breakdowns with different Poisson breakdown rates $\alpha_0$ and $\alpha$ for the empty period of the system and the nonempty period of the system, respectively. When the server breaks down, it will be repaired immediately by a repair facility attended by $R$ repairmen. The repair times of the servers are assumed to follow a negative exponential distribution with different repair rates $\beta_0$ and $\beta$ corresponding to whether the server breaks down in the empty period of the system and the nonempty period of the system. We study not only some queueing problems of the system, but also some reliability problems of the servers. By using the partitioned block matrix method, we solved the steady-state probability equations iteratively and derived the steady-state probabilities in a matrix form. Some performance measures of queueing and reliability are obtained. A cost model is developed to determine the optimum number of servers while the system availability is maintained at a certain level. The cost analysis is also investigated by numerical results.
2009, 5(3): 431-451 doi: 10.3934/jimo.2009.5.431 +[Abstract](2163) +[PDF](340.1KB)
Abstract:
This paper studies M/M/$c$/$c$ retrial queues, where $c$ servers are all identical. In the retrial queues, an arriving customer is served immediately if it finds an idle server upon arrival, otherwise the customer tries to enter the system after an exponentially distributed time independently of other customers. As is well known, it is a challenging problem to obtain an analytical solution for the stationary joint distribution of the numbers of retrial customers and busy servers in the M/M/$c$/$c$ retrial queue especially for $c \ge 3$. Under some technical assumptions, a few analytical solutions have been presented for $c \ge 3$. This paper derives analytical solutions for M/M/3/3 and M/M/4/4 retrial queues without such technical assumptions. Through many numerical examples, we show that the derived analytical solutions can be computed by a numerically stable algorithm.
2009, 5(3): 453-465 doi: 10.3934/jimo.2009.5.453 +[Abstract](1917) +[PDF](167.0KB)
Abstract:
In this paper, we study an M/M/2 queueing system with multiple vacations where the service rates of the servers are not identical. This queuing system has been analyzed as a quasi-birth and death process by Kumar and Madheswari (2005). However, by expressing the rate matrix explicitly, we have obtained a explicit expression of the stationary distribution of the queue length. The conditional stochastic decomposition properties of the queue length and the waiting time have been also established for such a system.
2009, 5(3): 467-479 doi: 10.3934/jimo.2009.5.467 +[Abstract](2029) +[PDF](308.2KB)
Abstract:
In this paper, we develop a discrete-time queueing model of fuzzy threshold-based space priority buffer management and study its performance under realistic conditions. It applies a matrix-analytic approach to analyze the relevant performance measure, including the packet loss probability of high-priority traffic and the packet loss probability of low-priority traffic. Intuitively, the fuzzy threshold adapts well to different input traffic conditions and packet loss rate requirements of high-priority packet, yielding a lower packet loss probability for low-priority packet.
2009, 5(3): 481-492 doi: 10.3934/jimo.2009.5.481 +[Abstract](1677) +[PDF](284.7KB)
Abstract:
For the battery-powered wireless stations, power saving is one of the significant issues in IEEE 802.11 wireless local area network (WLAN). Recently, Lei and Nilsson investigated the power save mode in IEEE 802.11 infrastructure mode by an M/G/1 queue with bulk service. They obtained the average packet delay and lower and upper bounds of the average Percentage of Time a station stays in the Doze state (PTD). In this paper, the further investigation of power save mode is done; simple derivation of the average and the variance of packet delay and the exact value of PTD are obtained. Numerical results show that our analytic results for PTD match quite well with simulation results. Using our performance analysis, we can find the maximal listen interval which minimizes the power consumption of a station while satisfying the required quality of service (QoS) on the average and the variance of packet delay.
2009, 5(3): 493-510 doi: 10.3934/jimo.2009.5.493 +[Abstract](1587) +[PDF](266.0KB)
Abstract:
It is well known that the end-to-end throughput in IEEE 802.11-based multihop wireless networks degrades due to the imprecise Extended Inter-Frame Space (EIFS) problem. The paper considers this throughput degradation issue by analyzing the end-to-end throughput in a backhaul-type wireless mesh network. Focusing on a three-node chain topology, we model it as a tandem queueing network with two nodes to derive the end-to-end throughput, and validate the analysis with ns-2 simulation. Numerical results show that the analytical results agree fairly well with simulation for a certain range of the offered load.
2009, 5(3): 511-524 doi: 10.3934/jimo.2009.5.511 +[Abstract](1914) +[PDF](277.1KB)
Abstract:
IEEE 802.16e is the latest broadband wireless access standard designed to support mobility. In mobile networks, how to control energy consumption is one of the most important issues for the battery-powered mobile stations. The standard proposes an energy saving mechanism that named "sleep mode" for conserving the power of the mobile stations. According to the operation mechanism of the sleep mode for downlink traffic in the type I power saving class, a discrete-time Geom/G/1 queueing model with close-down time and multiple vacations is built. By employing an embedded Markov chain method and Little's law, the average queue length, the average sojourn time and the average busy cycle of the queueing model are derived. Correspondingly, we get the performance measures of the energy saving rate and the average packet delay time for the sleep mode in the IEEE 802.16e. Finally, numerical results are given to demonstrate the dependency relationships between the system performance measures and the system parameters. Furthermore, a cost model is developed to determine the optimum length of the close-down time for minimizing the total system cost.
2009, 5(3): 525-540 doi: 10.3934/jimo.2009.5.525 +[Abstract](1759) +[PDF](357.7KB)
Abstract:
This paper presents the mathematical analysis of the truncated binary exponential backoff (TBEB) mechanism as a contention resolution for bandwidth requests in the broadcast polling and the multicast polling in the IEEE 802.16e. We derive the delay distribution and the loss probability of request packets in the TBEB over Gilbert-Elliot error channel, by analytic methods on the assumption of Bernoulli arrival process and the unsaturated condition. The optimal contention period of transmission opportunities for transmitting bandwidth requests can be obtained while satisfying QoS on delay bound and loss bound. Furthermore, we find the utilization of transmission opportunity to see efficiency of the bandwidth. Numerical examples show that the analytical results are well-matched with simulations, and the performance evaluations in the broadcast polling and multicast polling are compared on the mean delay, the loss probability and the utilization of transmission opportunity. Numerical results address that the multicast polling with more groups has better performance than the broadcast polling in the sense of shorter delay, lower loss probability and higher utilization of transmission opportunity.
2009, 5(3): 541-552 doi: 10.3934/jimo.2009.5.541 +[Abstract](1692) +[PDF](415.7KB)
Abstract:
In this paper, we analyze the stochastic characteristics of the measured video telephony service traffic and propose a mathematical model of the video telephony service traffic based on the analyzed stochastic characteristics. From our analysis, a voice traffic can be modelled by a renewal process with deterministic inter-arrival times and fixed packet size. On the other hand, a video traffic is modelled by an on and off source, where on and off periods are according to gamma distributions with respective parameters. Using the mathematical model, we estimate the required bandwidth to satisfy a given Quality of Service (QoS) requirement for the video telephony service traffic. To show the validity of our analysis, numerical studies with the NS-2 simulator are provided.
2009, 5(3): 553-567 doi: 10.3934/jimo.2009.5.553 +[Abstract](1581) +[PDF](199.5KB)
Abstract:
In this paper, we consider downlink transmission in a cellular wireless network, where a base station communicates with multiple mobile stations~(MSs) over Nakagami-$m$ fading channels. MSs are classified into two classes, and each class has its own minimum ergodic rate requirement. We propose an opportunistic scheduling and admission control scheme that aims at guaranteeing minimum ergodic rates for all MSs in the network. In order to maintain fairness among MSs in the same class and reduce the feedback load on the uplink of the network, our proposed scheme uses normalized SNR thresholds and exploits multiuser diversity with limited feedback. In our analysis, we give a formula by which we can easily check whether an incoming MS, who requests to join a class in the network, can be accepted or not. For accepted MSs in the network, we obtain the values of thresholds with which all MSs in the network can be guaranteed respective minimum ergodic rate requirements. Through numerical studies and simulations, we confirm the validity of our scheme and analysis, and show the usefulness of our scheme.
2009, 5(3): 569-584 doi: 10.3934/jimo.2009.5.569 +[Abstract](1707) +[PDF](300.5KB)
Abstract:
Herein is presented a human resource management system based on a working time account (WTA) in which accumulated hours expire after a certain date, whether those owed by the employee to the company, or vice versa. The condition of hours-expiry limits flexibility but protects workers. The consideration of this feature enables modelling of many current industrial scenarios, at the expense of complicating the use of WTAs and hugely increasing the size of the models. A staff planning problem from the services industry is modelled and solved through mathematical programming, and the approach is shown to be efficient for realistic staff sizes. Lastly, a variety of scenarios are presented, for which the financial benefit generated by WTAs is calculated and possible compensations for workers are explored.
2009, 5(3): 585-601 doi: 10.3934/jimo.2009.5.585 +[Abstract](2094) +[PDF](201.2KB)
Abstract:
In this paper, we present a penalty function with objective parameters for inequality constrained optimization problems. We prove that this type of penalty functions has good properties for helping to solve inequality constrained optimization problems. Moreover, based on the penalty function, we develop an algorithm to solve the inequality constrained optimization problems and prove its convergence under some conditions. Numerical experiments show that we can obtain a satisfactorily approximate solution for some constrained optimization problems as the same as the exact penalty function.
2009, 5(3): 603-613 doi: 10.3934/jimo.2009.5.603 +[Abstract](1841) +[PDF](178.6KB)
Abstract:
Complementarity problems over symmetric cones (SCCP) can be reformulated as the global minimization of a certain merit function. The coerciveness of the merit function plays an important role in this class of methods. In this paper, we introduce a class of merit functions which contains the Fischer-Burmeister merit function and the natural residual merit function as special cases, and prove the coerciveness of this class of merit functions under some conditions which are strictly weaker than the assumption that the function involving in the SCCP is strongly monotone and Lipschitz continuous. Based on the introduced merit function, we propose another class of merit functions which is an extension of Fukushima-Yamashita merit function. We investigate the coerciveness of the generalized Fukushima-Yamashita merit function under a condition which is strictly weaker than the assumption that the function involving in the SCCP is weakly coercive. The theory of Euclidean Jordan algebras is a basic tool in our analysis.
2009, 5(3): 615-628 doi: 10.3934/jimo.2009.5.615 +[Abstract](1622) +[PDF](154.5KB)
Abstract:
We propose a dual model of a multi-criteria network equilibrium model and establish a primal-dual relationship between the network model and its dual model under certain generalized monotonicity assumptions. By using Gerstewitz's function, we obtain the primal-dual relationship without any convexity assumptions. As an application of the dual model, we derive an existence result for the network model.
2009, 5(3): 629-649 doi: 10.3934/jimo.2009.5.629 +[Abstract](2192) +[PDF](226.9KB)
Abstract:
This paper presents a new mixed integer non-linear fractional programming model for multi-commodity, multi-period, budget constrained and capacitated global supply chain design problem. Our model simultaneously optimizes the facility location, capacity acquisition, and production-distribution decisions so as to maximize the profitability of the total investment over a planning horizon. The model is also compared with the profit-maximization model and the cost-minimization model. A branch-and-bound method and a rounding heuristic algorithm are developed to tackle the problem at hand. The computational results of solving 30 instances generated randomly show that our proposed model differs fundamentally from the other models and the rounding heuristic algorithm provides an efficient solution.
2009, 5(3): 651-669 doi: 10.3934/jimo.2009.5.651 +[Abstract](1862) +[PDF](221.1KB)
Abstract:
We present a nonlinear Lagrangian method for nonconvex semidefinite programming. This nonlinear Lagrangian is generated by a Löwner operator associated with Log-Sigmoid function. Under a set of assumptions, we prove a convergence theorem, which shows that the nonlinear Lagrangian algorithm is locally convergent when the penalty parameter is less than a threshold and the error bound of the solution is proportional to the penalty parameter.
2009, 5(3): 671-682 doi: 10.3934/jimo.2009.5.671 +[Abstract](1600) +[PDF](1329.2KB)
Abstract:
In this paper, the problem of deteriorating performance of speech recognition under very low signal-to-noise ratios (SNR) is considered. In particular, for a given pre-trained speech recognizer and for a finite set of speech commands, we show that popular noise reduction methods have a mixed performance in speech recognition accuracy under very low SNR. Although most noise reduction methods are attempting to reduce speech distortion or to increase noise suppression, it does not necessarily improve speech recognition accuracy very much due to the complexity of the recognizer. We propose a new hybrid algorithm to optimize on the speech recognition accuracy directly by mixing different noise reduction methods together. We show that this method can indeed improve the accuracy significantly.

2018  Impact Factor: 1.025

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