2007
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Yard Crane Pools and Optimum Layouts for Storage Yards of Container Terminals
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2
As more and more container terminals open up all over the world, competition for business is becoming very intense for container terminal operators. They are finding out that even to keep their existing Sea Line customers, they have to make them happy by offering higher quality service. The quality of service they can provide depends on their operating policies and the design of the terminal layout. Existing layouts based on designs prepared a long time ago pose inherent limitations. We summarize some of these problems, and report on newer operating policies and designs which can help improve performance.
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199


Katta G.
Murty
Department of Industrial and Operations Engineering
University of Michigan Ann Arbor, MI 481092117, USA
Department of Industrial and Operations Engineerin
Iran
Container Terminals
EXSY (export storage yards)
YC (yard cranes)
Crane clashing
Crane overloading
Crossgantrying
Congestion
QC (quay crane) rate
Storage space allocation policy
YC scheduling
Investment in cranes
Storage blocks and their optimum size
YC pools
[[1] Borovits I., EinDor P. (1975), Computer simulation of a seaport container terminal; Simulation 25;##[2] Dekker R., Voogd P., van Asperen E. (2006), Advanced methods for container stacking; OR Spectrum##28(4); 563586.##[3] Hartmann S. (2004), Generating scenarios for simulation and optimization of container terminal##logistics; OR Spectrum 26(2); 171192.##[4] Kozan E. (1997), Comparison of analytical and simulation planning models of seaport container##terminals; Transportation Planning and Technology 20; 235248.##[5] Lee T.W., Park N.K., Lee D.W. (2003), A simulation study for the logistics planning of a container##terminal in view of SCM; Maritime Policy & Management 30; 243254.##[6] Linn R., Liu J.Y., Wan Y.W., Zhang C., Murty K.G. (2003), Rubber tired gantry crane deployment for##container yard operation; Computers & Industrial Engineering 45(3); 429442.##[7] Linn R.J., Zhang C.Q. (2003), A heuristic for dynamic yard crane deployment in a container terminal;##IIE Transactions 35(2); 161174.##[8] Meersmans P.J.M., Dekker R. (2001), Operations research supports container handling; Econometric##Institute Report EI 200122.##[9] Murty K.G., Liu J., Wan Y.W., Linn R. (2005), A decision support system for operations in a container##terminal; Decision Support Systems 39(3); 309332.##[10] Murty K.G., Wan Y. W, Liu J., Tseng M.M., Leung E., Lai K.K., Chiu H.W.C. (2005), Hong Kong##International Terminals Gains Elastic Capacity Using a DataIntensive DecisionSupport System;##Interfaces 35(1); 6175.##[11] Nevins M.R., Macal C.M., Joines J.C. (1998), A discreteevent simulation model for seaport##operations; Simulation 70(4); 213223.##[12] Petering M.E.H. (2007), Design, analysis, and realtime control of material handling systems in##container terminals; Ph.D. dissertation, IOE Department, University of Michigan, Ann Arbor.##[13] Petering M.E.H., Murty K.G. (2006), Simulation analysis of algorithms for container storage and yard##crane scheduling at a container terminal; Proceedings of the Second International Intelligent Logistics##Systems Conference, Brisbane, Australia.##[14] Petering M.E.H., Wu Y., Li W., Goh M., Murty K.G., de Souza R. (2006), Simulation analysis of yard##crane routing systems at a marine container transshipment terminal; Proceedings of the International##Congress on Logistics and Supply Chain Management Systems, Kaohsiung, Taiwan.##[15] Shabayek A.A., Yeung W.W. (2002), A simulation model for the Kwai Chung container terminals in##Hong Kong; European Journal of Operational Research 140(1); 111.##[16] Silberholz M.B., Golden B.L., Baker E.K. (1991), Using simulation to study the impact of work rules##on productivity at marine container terminals; Computers & Operations Research 18(5); 433452.##[17] Steenken D., Vo S., Stahlbock R. (2004), Container terminal operation and operations research  a##classification and literature review; OR Spectrum 26(1); 349.##[18] Zhang C., Wan Y.W., Liu J., Linn R.J. (2002), Dynamic crane deployment in container storage yards;##Transportation Research Part B: Methodological 36(6); 537555.##]
OneforOne Period Policy and its Optimal Solution
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2
In this paper we introduce the optimal solution for a simple and yet practical inventory policy with the important characteristic which eliminates the uncertainty in demand for suppliers. In this new policy which is different from the classical inventory policies, the time interval between any two consecutive orders is fixed and the quantity of each order is one. Assuming the fixed ordering costs are negligible, lead times are constant, and demand forms a Poisson process, we use queuing theory concepts to derive the longrun average total inventory costs, consisting of holding and shortage costs in terms of the average inventory. We show that the total cost rate has the important property of being entirely free of the lead time. We prove that the average total cost rate is a convex function and thus has a unique solution. We, then derive the relation for the optimal value of the time interval between any two consecutive orders. Finally we present a numerical example to compare the performance of this new policy with the classical oneforone ordering policy. The provided example intends to reexamine the optimality of (s, S) policy in continuous review inventory models as well to establish the fact that even for the case where demand forms a Poisson process the optimality does not hold.
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200
217


Rasoul
Haji
Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran
Department of Industrial Engineering, Sharif
Iran


Alireza
Haji
Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran
Department of Industrial Engineering, Sharif
Iran
Inventory control
One for one period policy
(s
S) Policy
Queuing system
Poisson Demand
[[1] Andersson J., Melchiors P. (2001), A twoechelon inventory model with lost sales;##International Journal of Production Economics 69(3); 307315.##[2] Archibald B.C. (1981), Continuous review (s, S) policies with lost sales; Management Science##27; 11711178.##[3] Axsäter S. (1990), Simple solution procedures for a class of twoechelon inventory problems;##Operation Research 38; 6469.##[4] Axsäter S. (1993), Exact and approximate evaluation of batchordering policies for twolevel##inventory systems; Operations .Research 41; 777785.##[5] Axsäter S. (2003), Approximate optimization of a twolevel distribution inventory system;##International Journal of Production Economics 8182; 545553.##[6] Axsäter S., Forsberg R., Zhang W.F. (1994), Approximating general multiechelon inventory##systems by Poisson models; International Journal of Production Economics 35; 201206.##[7] Axsäter S., Zhang W.F. (1999), A joint replenishment policy for multiechelon inventory##control; International Journal of Production Economics 59; 243250.##[8] Beckman M. (1961), An inventory model for arbitrary interval and quantity distribution of##demand; Management Science 8; 3557.##[9] Federgruen A., Zheng Y. S. (1992), An efficient algorithm for computing an optimal (r, Q)##policy for continuous review stochastic inventory systems; Operations Research 40; 808812.##[10] Forsberg R. (1995), Optimization of orderuptoS policies for twolevel inventory systems##with compound Poisson demand; European Journal of Operational Research 81; 143153.##[11] Forsberg, R. (1996), Exact evaluation of (R,Q) policies for twolevel inventory systems with##Poisson demand; European Journal of Operational Research; 96; 130138.##[12] Forsberg R. (1997), Evaluation of (R, Q) policies for twolevel inventory systems with##generally distributed customer interarrival times; European Journal of Operational##Research 99; 401411.##[13] Ganeshan R. (1999), Managing supply chain inventories: A multiple retailer, one warehouse,##multiple supplier model; International Journal of Production Economics 59; 341354.##[14] GhalebsazJeddi B, Shultes B. C, Haji R. (2004), A multiproduction continuous review##inventory system with stochastic demand, backorders, and a budget constraint; European##Journal of Operational Research 158; 456469.##[15] Graves S. (1985), A multiechelon inventory model for a repairable item with one–forone##replenishment; Management Science 31; 12471256.##[16] Hadley G., Whitin. T. (1963), Analysis of inventory systems. Prentice Hall. Englewood##Cliffs. NJ.##[17] Haji R., Pirayesh M., Baboli A. (2006), A new replenishment policy in a twoechelon##inventory system with stochastic demand, International Conference on Service System and##Service ManagementICSSSM’06 Proceeding, 256–260 Troyes, France, 2527 October##[18] Iglehart. D. (1963), Optimality of (s, S) policies in the infinite horizon dynamic inventory##problem; Management Science 9; 259267.##[19] Johnson L.A., Montgomery D.C. (1974), Operation research in production planning,##scheduling, and inventory control, John Wiley & Sons, New York.##[20] Kruse W. K. (1980), Waiting time in an (S1, S) inventory system with arbitrary distributed##lead times; Operations Research 28; 348352.##[21] Kruse W. K. (1981), Waiting time in a continuous review (s, S) inventory system with##constant lead times; Operations Research 29; 202206.##[22] Lee H.L., Moinzadeh K. (1987a), Twoparameter approximations for multiechelon##repairable inventory models with batch ordering policy; IIE Transactions 19; 140149.##[23] Lee H.L., Moinzadeh K. (1987b), Operating characteristics of a twoechelon inventory##system for repairable and consumable items under batch ordering and shipment policy; Naval##Research Logistics Quarterly 34; 356380.##[24] Love S. (1979), Inventory control, McGrawHill Book Company, New York##[25] Marklund J., (2002), Centralized inventory control in a twolevel distribution system with##Poisson demand; Naval Research Logistics 49;798822.##[26] Matta K.F., Sinha D. (1995), Policy and cost approximations of twoechelon distribution##systems with a procurement cost at the higher echelon; IIE Transactions 27(5); 646656.##[27] Moinzadeh K. (2001), An improved ordering policy for continuous review inventory systems##with an arbitrary interdemand time distributions; IIE Transactions 33; 111118.##[28] Moinzadeh K. (2002), A multiechelon inventory system with information exchange,##Management Science 48(3); 414426.##[29] Moinzadeh; K., Lee H.L. (1986), Batch size and stocking levels in multiechelon repairable##systems; Management Science 32; 15671581.##[30] Nahmias S. (1976), On the equivalence of three approximate continuous review inventory##model; Naval Research Logistics Quarterly 23; 3138.##[31] Nahmias S. (2005), Production and operations analysis; 5th edition, McGrawHill/Irwin; New##[32] Nahmias S., Smith S.A. (1994), Optimizing inventory levels in a twoechelon retailer system##with partial lost sales; Management Science 40; 582596.##[33] Ross S. M. (1993), Introduction to probability models Fifth Edition, Academic press, New##[34] Sahin I. (1979), On the stationary analysis of continuous review (s, S) inventory systems with##constant lead times; Operations Research 27; 717729.##[35] Sahin I. (1982), On the objective function behavior in (s, S) inventory models; Operations##Research 30; 709724.##[36] Sahin I. (1990), Regenerative inventory systems SpringerVerlag, New York. NY.##[37] Scarf H. E. (1960), The optimality of (s, S) policies in the dynamic inventory problem. In##Mathematical Methods in the social Sciences. Stanford University Press. Stanford. CA.##[38] Schultz C. R. (1989), Replenishment delays for expensive slowmoving items; Management##Science 35; 14541462.##[39] Seo Y., Jung S,. Hahm J. (2002), Optimal reorder decision utilizing centralized stock##information in a twoechelon distribution system; Computers & Operations Research 29;##[40] Sherbrooke C. C. (1968), METRIC: a multiechelon technique for recoverable item control;##Operations Research 16; 122141.##[41] Sivlazian B. D. (1974), A continuous review (s, S) inventory system with arbitrary interval##distribution between unit demand; Operations Research 22; 6571##[42] Tijms H.C. (1986), Stochastic modeling and analysisA computational approach. John Wiley##and Sons, New York.##[43] Zheng Y. S. (1992), On properties of stochastic inventory systems; Management Science 38;##[44] Zipkin P. (1986a), Stochastic lead times in continuous review inventory systems; Naval##Research Logistics Quarterly 35; 763774.##[45] Zipkin P. (1986b), Inventory service level measures: convexity and approximations;##Management Science 32; 975981.##[46] Zipkin P. H. (2000), Foundation of inventory management. McGrawHill, New York##]
Quality Loss Function – A Common Methodology for Three Cases
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2
The quality loss function developed by Genichi Taguchi considers three cases, nominalthebest, smallerthebetter, and largerthebetter. The methodology used to deal with the largerthebetter case is slightly different than the other two cases. This research employs a term called targetmean ratio to propose a common formula for all three cases to bring about similarity among them. The targetmean ratio can take different values representing all three cases to bring consistency and simplicity in the model. In addition, it eliminates the assumption of target performance at an infinite level and brings the model closer to reality. Characteristics such as efficiency, coefficient of performance, and percent nondefective are presently not largerthebetter characteristics due to the assumption of target performance at infinity and the subsequent necessary derivation of the formulae. These characteristics can also be brought under the category of the largerthebetter characteristics. An example of the efficiency of prime movers is discussed to illustrate that the efficiency can also be considered as a largerthebetter characteristic. A second example is presented to suggest the subtle differences between both methodologies.
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Networked quality loss
Signaltonoise ratio
Targetmean ratio
[[1] Ferreira O.C., http://ecen.com/content/eee7/motoref.htm, April 2005.##[2] Fowlkes W.Y., Creveling C.M. (1995), Engineering methods for robust product design; Addison##[3] Maghsoodloo S. (1991), The exact relationship of Taguchi's signalto noise ratio to his quality loss##function; Journal of Quality Technology 22(1); 5767.##[4] Phadke M. S. (1989), Quality engineering using robust design; PrenticeHall, Englewood Cliffs, New##[5] Taguchi G., Chowdhury S., Taguchi S. (1999), Robust engineering; McGrawHill.##[6] Taguchi G., Chowdhury S., Wu Y. (2004), Taguchi’s quality engineering handbook; Edition 2004, pp.##[7] Taguchi G., Elsayed A., Hsiang T. (1989), Quality engineering in production systems; McGrawHill##Publishing Company.##[8] Venkateswaren S. (2003), Warranty cost prediction using Mahalanobis Distance, MS Thesis,##University of MissouriRolla.##]
A OneStage TwoMachine Replacement Strategy Based on the Bayesian Inference Method
2
2
In this research, we consider an application of the Bayesian Inferences in machine replacement problem. The application is concerned with the time to replace two machines producing a specific product; each machine doing a special operation on the product when there are manufacturing defects because of failures. A common practice for this kind of problem is to fit a single distribution to the combined defect data, usually a distribution with an increasing hazard rate. While this may be convenient, it does not adequately capture the fact that there are two different underlying causes of failures. A better approach is to view the defect as arising from a mixture population: one due to the first machine failures and the other due to the second one. This allows one to estimate the various parameters of interest including the mixture proportion and the distribution of time between productions of defective products for each machine, separately. To do this, first we briefly introduce the data augmentation method for Bayesian inferences in the context of the finite mixture models. Then, we discuss the analysis of timetofailure data and propose an optimal decisionmaking procedure for machine replacement strategy. In order to demonstrate the application of the proposed method we provide a numerical example.
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235
250


Mohammad Saber
Fallah Nezhad
Department of Industrial Engineering, Sharif University of Technology
P.O. Box 113659414, Azadi Ave., Tehran, Iran
Department of Industrial Engineering, Sharif
Iran


Seyed Taghi
Akhavan Niaki
Department of Industrial Engineering, Sharif University of Technology
P.O. Box 113659414, Azadi Ave., Tehran, Iran
Department of Industrial Engineering, Sharif
Iran


Abdolhamid
Eshragh Jahromi
Department of Industrial Engineering, Sharif University of Technology
P.O. Box 113659414, Azadi Ave., Tehran, Iran
Department of Industrial Engineering, Sharif
Iran
Reliability
Weibull distribution
preventive maintenance
Bayesian inference
[[1] Box G.E.P., Tiao G.C. (1992), Bayesian inferences in statistical analysis; Wiley Classic Library##Edition; New York.##[2] Chen T.M., Popova E. (2000), Bayesian maintenance policies during a warranty period;##Communications in Statistics –Stochastic Models 16; 121142.##[3] Childress S., DurangoCohen P. (2005), On parallel machine replacement problems with general##replacement cost functions and stochastic deterioration; Naval Research Logistics 52; 409419.##[4] Damien P., Galenko A., Popova E., Hanson T. (2007), Bayesian semiparametric analysis for a single##item maintenance optimization; European Journal of Operational Research 182; 794805.##[5] Gupta A., Lawsirirat C. (2006), Strategically optimum maintenance of monitoringenabled multicomponent##systems using continuoustime jump deterioration model; Journal of Quality in##Maintenance Engineering 12; 306329.##[6] Hamada M., Martz H.F., Reese C.S., Graves T., Johnson V., Wilson A.G. (2004), A fully Bayesian##approach for combining multilevel failure information in fault tree quantification and optimal followon##resource allocation; Reliability Engineering and System Safety 86; 297305.##[7] Hritonenko N., Yatsenko Y. (2007), Optimal equipment replacement without paradoxes: A continuous##analysis; Operations Research Letters 35; 245250.##[8] Jardine A.K.S., Banjevic D., Makis V. (1997), Optimal replacement policy and the structure of##software for conditionbased maintenance; Journal of Quality in Maintenance Engineering 3; 109119.##[9] Mann L., Saxena A., Knapp G. (1995), Statisticalbased or conditionbased preventive maintenance;##Journal of Quality in Maintenance Engineering 1; 4659.##[10] Mazzuchi T.A., Soyer R. (1996), A Bayesian perspective on some replacement strategies; Reliability##Engineering and System Safety 51; 295303.##[11] Merrick J.R.W., Soyer R., Mazzuchi T.A. (2003), A Bayesian semiparametric analysis of the##reliability and maintenance of machine tools; Technometrics 45; 5869.##[12] Mobley K.R (1989), An introduction to predictive maintenance; ButterworthHeinemann, New York.##[13] Moubray J. (1990), Reliability centered maintenance; ButterworthHeinemann, Oxford.##[14] Nair V.N., Tang B., Xu L. (2001), Bayesian inference for some mixture problems in quality and##reliability; Journal of Quality Technology 33; 1628.##[15] Saranga H. (2002), A dynamic opportunistic maintenance policy for continuously monitored systems;##Journal of Quality in Maintenance Engineering 8; 92105.##[16] Sethi S.P., Sorger G., Zhou X.Y. (2000), Stability of realtime lotscheduling and machine replacement##policies with quality levels; IEEE Transactions on Automatic Control 45; 21932196.##[17] Sherwin J.D. (1999), Agebased opportunity maintenance; Journal of Quality in Maintenance##Engineering 5; 221235.##[18] Sherwin J.D., AlNajjar B. (1999), Practical models for conditionbased monitoring inspection##intervals; Journal of Quality in Maintenance Engineering 5; 203209.##[19] SinuanyStern Z.S. (1993), Replacement policy under partially observed Markov process;##International Journal of Production Economics 29; 159166.##[20] SinuanyStern Z.S., David I., Biran S. (1997), An efficient heuristic for a partially observable Markov##decision process of machine replacement; Journal of Computers in Operations Research 24; 117126.##[21] Tanner M.A., Wong W.H. (1987), The calculation of posterior distributions by data augmentation;##Journal of the American Statistical Association 82; 528540.##[22] Tsang A. (1995), Conditionbased maintenance: tools and decision making; Journal of Quality in##Maintenance Engineering 1; 317.##[23] ValdezFlorez C., Feldman R. (1989), A survey of preventive maintenance models for stochastically##deteriorating single unit systems; Naval Research Logistics 36; 419446.##[24] Wang C.H., Hwang S.L. (2004), A stochastic maintenance management model with recovery factor;##Journal of Quality in Maintenance Engineering 10; 154164.##[25] Wilson J.G., Popova E. (1998), Bayesian approaches to maintenance intervention; In Proceedings of##the section on Bayesian Science of the American Statistical Association, 278284.##[26] Zhou X., Xi L., Lee J. (2006), A dynamic opportunistic maintenance policy for continuously##monitored systems; Journal of Quality in Maintenance Engineering 12; 294305##]
Applying the MahalanobisTaguchi System to Vehicle Ride
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2
The Mahalanobis Taguchi System is a diagnosis and forecasting method for multivariate data. Mahalanobis distance is a measure based on correlations between the variables and different patterns that can be identified and analyzed with respect to a base or reference group. The Mahalanobis Taguchi System is of interest because of its reported accuracy in forecasting small, correlated data sets. This is the type of data that is encountered with consumer vehicle ratings. MTS enables a reduction in dimensionality and the ability to develop a scale based on MD values. MTS identifies a set of useful variables from the complete data set with equivalent correlation and considerably less time and data. This paper presents the application of the MahalanobisTaguchi System and its application to identify a reduced set of useful variables in multidimensional systems.
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259


Elizabeth A.
Cudney
University of Missouri – Rolla, Rolla, Missouri 65409 USA
University of Missouri – Rolla, Rolla, Missouri
Iran


Kioumars
Paryani
Lawrence Technological University, Southfield, Massachusetts 02139 USA
Lawrence Technological University, Southfield,
Iran


Kenneth M.
Ragsdell
University of Missouri – Rolla, Rolla, Missouri 65409 USA
University of Missouri – Rolla, Rolla, Missouri
Iran
MahalanobisTaguchi system (MTS)
Mahalanobis distance (MD)
Mahalanobis space
Pattern Recognition
Signaltonoise ratio
Orthogonal array
[[1] Asada M. (2001), Wafer yield prediction by the MahalanobisTaguchi system; IEEE International##Workshop on Statistical Methodology 6; 2528.##[2] Fowlkes W.Y., Creveling C.M. (1995), Engineering methods for robust product design; Addison##Wesley, Reading, MA.##[3] Hong J., Cudney E.A., Taguchi G., Jugulum R., Paryani K., Ragsdell K. (2005), A comparison study of##MahalanobisTaguchi system and neural network for multivariate pattern recognition, ASME IMECE,##Orlando, FL.##[4] Jugulum R., Monplaisir L. (2002), Comparison between MahalanobisTaguchi system and artificial##neural networks; Journal of Quality Engineering Society 10(1); 6073.##[5] Kiemele M.J., Schmidt S.R., Berdine R.J. (1999), Basic statistics: Tools for continuous improvement;##Air Academy Press, Colorado Springs, CO.##[6] Lande U., Mahalanobis distance: A theoretical and practical approach,##http://biologi.uio.no/fellesavdelinger/finse/spatialstats/Mahalanobis%20distance.ppt, July 11, 2004.##[7] Manly B.F.J. (1994), Multivariate statistical methods: A primer; Chapman & Hall, London.##[8] Taguchi G., Jugulum R. (2002), The MahalanobisTaguchi strategy; John Wiley & Sons, Inc., New##[9] Wu Y. (2004), Pattern recognition using Mahalanobis distance; Journal of Quality Engineering Forum##12 (5); 787795.##]
A NonPreemptive TwoClass M/M/1 System with Prioritized RealTime Jobs under EarliestDeadlineFirst Policy
2
2
This paper introduces an analytical method for approximating the performance of a twoclass priority M/M/1 system. The system is fully nonpreemptive. More specifically, the prioritized class1 jobs are realtime and served with the nonpreemptive earliestdeadlinefirst (EDF) policy, but despite their priority cannot preempt any non realtime class2 job. The waiting class2 jobs can only be served from the time instant that no class1 job is in the system. The service discipline of the class2 jobs is FCFS. The required mean service times may depend on the class of the jobs. The realtime jobs have exponentially distributed relative deadlines until the end of service. The system is approximated by a Markovian model in the long run, which can be solved numerically using standard Markovian solution techniques. The performance measures of the system are the loss probability of the class1 jobs and the mean sojourn (waiting) time of the class2 jobs. Comparing the numerical and simulation results, we find that the existing errors are relatively small.
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280
Approximation methods
Earliestdeadlinefirst (EDF) policy
Nonpreemptive services
Queuing
Realtime jobs
Twoclass priority M/M/1 system
[[1] Baccelli F., Boyer P., Hebuterne G. (1984), Singleserver queues with impatient customers; Advanced##Applied Probability 16; 887905.##[2] Barrer D.Y. (1957), Queueing with impatient customers and ordered service; Operational Research5;##[3] Bernat G., Burns A., Llamosi, A. (2001), Weakly hard realtime systems; IEEE Transactions on##Computers 50(4); 308321.##[4] Boxma O.J., Wall P.R. (1994), Multiserver queues with impatient customers; Proceedings of the 14th##International Teletraffic Congress, 14, Antibes, France, pp 743756.##[5] Brandt A. Brandt M. (1999a), On the M(n)/M(n)/s Queue with impatient calls; Performance##Evaluation 35; 118.##[6] Brandt A. Brandt M. (1999b), On a twoqueue priority system with impatience and its application to a##call center; Methodology and Computing in Applied Probability 1; 191210.##[7] Brandt A. Brandt M. (2002), Asymptotic results and a Markovian approximation for the##M(n)/M(n)/s+GI system; Queueing Systems 41; 7394.##[8] Brandt A. Brandt M. (2004), On the twoclass M/M/1 system under preemptive resume and impatience##of the prioritized customers; Queueing Systems 47(12), 147168.##[9] CANCIA, CAN specification 2.0 Part B, http://www.cancia.org/downloads/ ciaspecifications, 1992.##[10] Choi B.D., Kim B., Chung J. (2001), M/M/1 Queue with impatient customers of higher priority;##Queueing Systems 38; 4966.##[11] Daley D.J. (1965), General customer impatience in queue GI/G/1; Journal of Applied Probability 2;##[12] Dolev S. Keizelman A. (1999), Nonpreemptive realtime scheduling of multimedia tasks; RealTime##Systems 17(1); 23–39.##[13] Doytchinov B., Lehoczky J., Shreve S. (2001), Realtime queues in heavy traffic with earliestdeadline##first queue discipline; Annals of Applied Probability 11; 332379.##[14] EN 50170, General purpose field communication system, In European Standard, CENELEC, 1996.##[15] George L., Muhlethaler P., Rivierre N. (1995), Optimality and nonpreemptive realtime scheduling##revisited; Rapport de Recherche RR2516, INRIA, Le Chesnay Cedex, France.##[16] George L., Rivierre N., Spuri M. (1996), Preemptive and nonpreemptive realtime uniprocessor##scheduling; Rapport de Recherche RR2966, INRIA, Le Chesnay Cedex, France.##[17] Hong J., Tan X., Towsley D. (1989), A performance analysis of minimum laxity and earliest deadline##scheduling in a realtime system; IEEE Transactions on Computers 38(12); 17361744.##[18] Jaiswal N. (1968), Priority queues; Academic Press, New York.##[19] Kargahi M., Movaghar A. (2004), A method for performance analysis of earliestdeadlinefirst##scheduling policy; Proceedings of the 2004 IEEE International Conference on Dependable Systems##and Networks, Florence, Italy, pp 826834.##[20] Kargahi M., Movaghar A. (2005), Nonpreemptive earliestdeadlinefirst scheduling policy: A##performance study; Proceedings of IEEE International Symposium on Modeling, Analysis, and##Simulation of Computer and Telecommunication Systems, Georgia, Atlanta, USA, pp 201210.##[21] Kargahi M., Movaghar A. (2006), A method for performance analysis of earliestdeadlinefirst##scheduling policy; Journal of Supercomputing 37(2); 197222.##[22] Kargahi M., Movaghar A. (2007), A multiprocessor system with nonpreemptive earliest deadline first##scheduling policy: A performability study; Journal of Industrial and Systems Engineering 1(1); 3755.##[23] Kruk L., Lehoczky J., Shreve S., Yeung S.N. (2003), Multipleinput heavytraffic realtime queues;##Annals of Applied Probability 13(1); 5499.##[24] Kruk L., Lehoczky J.P., Shreve S., Yeung S.N. (2004), Earliestdeadlinefirst service in heavytraffic##acyclic networks; Annals of Applied Probability 14(3); 13061352.##[25] Lehoczky J.P. 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