REFERENCES. [3] Ancker Jr. C. J., Gafarian A. V., Some queueing problems with balking and reneging, I. Operations Research 11, pp , 1963.

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1 REFERENCES [1] Abou El-Ata M. O., Hariri A. M. A., The M/M/C/N queue with balking and reneging Computers and Operations Research 19, pp , [2] Abou-El-Ata M. O., New approach for the moments of the simple birth-death processes and discrete distribution II, In Faculty of Education Journal, Ain Shams Univ. Press, Cairo, Egypt, pp , [3] Ancker Jr. C. J., Gafarian A. V., Some queueing problems with balking and reneging, I. Operations Research 11, pp , [4] Ancker Jr. C. J., Gafarian A. V., Some queueing problems with balking and reneging, II. Operations Research 11, pp , [5] Ancker Jr. C. J., Gafarian A. V., "Queueing with Impatient Customers who Leave at Random", J. Indust. Eng. 13, pp , [6] Ancker Jr. C. J., Gafarian A. V., "Queueing with Reneging and Multiple Hetero-geneous servers, Naval Res. Log. Quart. 10, pp , [7]. Ancker Jr. C. J., Gafarian A. V., "Queuing with Reneging and Multiple Heterogeneous Servers", SP-372, System Development Corporation, pp , [8] Avi-Itzhak B., Naor P., Some queueing problems with the service station subject to breakdown, Oper. Res., 11, pp , [9] Baccelli F., Boyer P., Hebuterne G., Single-server queues with impatient customers, Adv. Appl. Prob. 16, pp ,

2 [10] Bailey N. T. J., Study of Queues and Appointment Systems in Out- patient Departments with Special Reference to Waiting Times, J. Roy. Statist. Soc. Ser. B.14, pp , [11] Bailey N. T. J., A Continuous Time Treatment of a Single Queue Using Generating Functions, J. Roy. Statist. Soc. Ser. B.16, pp , [12] Barrer D.Y., Queuing with impatient customers and ordered service, Oper. Res. 5, pp , [13] Bbocmeyer E., Halstrom H. L., Jensen A., The Life and Works of A. K. Erlang, Copenhagen Telephone Company, [14] Brumelle S. L., A Generalization of Erlang's Loss System to State Dependent Arrival and Service Rates, Math. Opns. Res. 3, pp ,1978. [15] Boots N.K., Tijms H., A multiserver queueing system with impatient customers,management Sci. 45, pp , [16] Champernowne D. G., An Elementary Method of Solution of the Queueing Problem with a Single Server and a Constant Parameter, J. Roy. Statist. Soc. Ser. B.18, pp , [17] Cheng X., Akyildiz I. F., A finite buffer two class queue with different scheduling and pushout schemes, Proceedings of IEEE INFOCOM 92, pp , [18] Choi B.D., Kim B., Chung J., M/M/1 queue with impatient customers of higher priority, Queueing Systems 38, pp [19] Cohen J.W., The single server queue, North-Holland, Amsterdam [20] Cooper R. B., Introduction to Queueing Theory 2 nd ed. New York, North Holland,

3 [21] Cox D. R., Walter L. Smith, Queues, p. 44, Wiley, New York, [22] Crommelin C. D., Delay Probability Formulae When the Holding Times Are Constant, P. O. Elec. Eng. J. 25, pp , [23] Daley D.J., General customer impatience in the queue GI/G/1, J. Appl. Prob. 2, pp , [24] Doig Alison, A Bibliography on the Theory of Queues, Biometrika 44, pp , [25] Elion S., A Simple Proof of L= λ W, Oper. Res. 17, pp , [26] Erlang A. K., The Theory of Probabilities and Telephone Conservations, Nyt Tidsskrift Mat. B 20, pp , [27] Erlang A. K., Soutions of Some Problems in the Theory of Probabilities of Significance in Automatic Telephone Exchanges, Electroteknikeren (Danish) 13, pp. 5-13, [English Translation, P. O. Elec. Eng. J. 10, pp ( ).] [28] Feller W., An Introduction to Probability Theory and its Applications, New York: John Wiley and Sons, vol I., [29] Fry T. C., Probability and its Engineering Uses, Princeton, NJ: Van Nostrand, [30] Gail, H.R., S.L.Hantler, B.A.Taylor., Analysis of a non-preemptive priority multiserver queue, Advances in Applied Probability. 20, No.4, pp , [31] Gail, H.R., S.L.Hantler, B.A.Taylor, On preemptive Markovian queue with multiple servers and two priority classes, Mathematics Operations Research. 17, No.2, pp , [32] Gaver D. P., Junior, A waiting line with interrupted service, including priorities, J. Roy. Stat. Soc., B 24, pp ,

4 [33] Gnedenko B.V., Kovalenko I.N., Introduction to queueing theory, Israel Program for Scientific Translations, Jerusalem [34] Gravey A., Boyer P., Hebuterne G., Tagging versus strict rate enforcement in ATM networks, Proceedings of IEEE GLOBECOM 91, pp , [35] Gross D., Harris C. M., On One-for-One Ordering Inventory Policies with State-Dependent Leadtimes, Oper. Res. 19, pp , [36] Gross D., Harris C. M., Fundamentals of Queueing Theory, 2 nd ed. New York: Wiley, [37] Gross D., Harris C. M., Fundamentals of Queueing Theory, John Wiley & Sons, New York, [38] Haghighi A. M., Medhi J., Mohanty S. G., On a multi-server Markovian queueing system with balking and reneging,computers Ops Res. 13, pp , [39] Haight F. A., Queueing with balking, Biometrika 44, pp , [40] Haight F. A., Queueing with reneging, Metrika 2, pp , [41] Heyman D. P., The push-out priority queue discipline, Operations Research, vol.33, no. 2, pp , [42] Heyman D. P., Sobel M. J., Stochastic Models in Operations Research, Vol. I. McGraw-Hill, New York, [43] Homma T., "On a Certain Queuing Process", Rept. Statist. Application Research, Union Japanese Scientists and Engrs. 4, No. 1, [44] Jaiswal N. K., Priority Queues, New York, Academic Press,

5 [45] Kawata T., A problem in the theory of queues, Rep. Statist. Appl. Res. Un. Jap. Set. Engrs,3, pp , [46] Kao, E.P.C., K.S.Narayanan K.S., Computing steady state probabilities of a nonpreemptive priority queue, ORSA Journal on Computing, 2, pp , [47] Kao, E.P.C., Wilson S.D., Analysis of nonpreemptive priority queues with multiple servers and two priority classes. European Journal of Operational Research. 118, pp , [48] Keilson J., Queues subject to service interruption, Ann. Math. Statist., 33, pp , [49] Kella, O., Yechiali U., Waiting times in the non-preemptive priority M/M/c queue, Communications in Statistics - Stochastic Models, 1, pp , [50] Kendall D. G., Some Problems in the Theory of Queues, J. Roy Statist. Soc. Ser. B 13, pp , [51] Kendall D. G., Stochastic Processes Occuring in the Theory of Queues and Their Analysis by the Method of Imbedded Markov Chains, Ann. Math. Statist. 24, pp ,1953. [52] Kendall D. G., Some Recent Work and Further Problems in the Theory of Queues, Theory Prob. Appl. 9, pp.1-15, [53] Kendall D. G., Reuter G. E. H., The calculation of the ergodic projection for Markov chains and processes with a countable infinity of states, Acta Mathematica, 97, pp , [54] Kesten H., Runnen burg J.T., Priority Waiting Line Problems I, II, Koninkz, Ned Ankad, Wetenschap, Proc. Ser A 60, pp ,

6 [55] Khintchine A.Y., Mathematisches ϋber die Erwortung vor einemöffenthchen Schalter, Mat. Sb. 39, pp , [56] Kleinrock L., Queueing Systems, vol. 1:Theory, Wiely, New York, [57] Koenigsberg E, On Jockeying in Queues, Manage. Sci. 12, pp , [58] Kolmogorov A. N., Sur le problem d attente, Mat. Sb. 8, pp , [59] Koopman B. O., New mathematical methods in operations research, J. Opna. Res. Soc. of America, 1, pp. 3-9, [60] Lebebev A. V., Federova R. M., A Guide to Mathematical Tables, Pergamon Press, New York, pp , [61] Ledermann W., Reuter G. E., Spectral Theory for the Differential Equations of Simple Birth and Death Process, Phil. Trans. Roy. Soc. London Ser. A 246, pp , [62] Lindley D. V., The theory of queues with single server, Proc. Comb. Phil. Soc. 48, pp , [63] Little J. D. C., A Proof for the Queuing Formula L=λW, Oper. Res. 9, pp ,1961. [64] Miller B. I., A Queueing Reward System with Several Customer Classes, Manage, Sci. 16, pp ,1969. [65] Mitrani I., King P.J.B., Multiprocessor systems with preemptive priorities. Performance Evaluation1, pp , [66] Molina E. C., Application of the Theory of Probability to Telephone Trunking Problems, Bell Syst. Tech. J. 6, pp ,

7 [67] Morse P. M., Queues, Inventory and Maintenance, New York, Wiley, [68] Movaghar A., On queueing with customer impatience until the beginning of service, Queueing Systems 29, pp , [69] Palm C., Analysis of the Erlang Traffic Formulae for Busy Signal Arrangements, Ericsson Tech. 6, pp , [70] Parzen E., Stochastic Process, San Francisco: Holden-day, [71] Parzen E., Modern Probability and Its Applications, New York: Wiley, [72] Pollaczek F., Lösung eines Geometrischen Wahrsceinlichkeits-problems, Math. Z. 35, pp , [73] Pollaczek F., Über das Waterproblem, Math. Z. 38, pp , [74] Rao S.S., Queueing with balking and reneging in M/G/1 systems, Metrika 12, pp , [75] Reynolds J. F., The stationary solution of the multi-server queueing model with discouragement, Ops Res. 16, pp , [76] Riley, Vera, Bibliography of Queueing Theory, Operations Research for Management, Vol. II, Edited by J.F. McCloskey and F. V. Trefethen, Johns Hopkins Press, [77] Robert E., Reneging phenomenon of single channel queues, Mathematics of Operations Research 4(2), pp , [78] Saaty T. L., Elements of Queueing Theory with Applications, New York: McGraw Hill,

8 [79] Saaty T. L., Seven More Years of Queues: A Lament and a Bibliography, Nav. Res. Log. Quart. 13, pp , [80] Saaty T. L., Resume of Useful formulas in Queueing Theory, Opns. Res. 5, pp , [81] Singh V. P., Two server Markovian queues with balking: heterogeneous vs homogeneous servers, Ops Res. 18, pp , [82] Stanford R.E., Reneging phenomena in single channel queues, Math. Oper. Res. 4, pp , [83] Takacs L., Investigation of waiting time problems by reduction to Markov processes. Ada Math. Acad. Sd. Hungary, 6, pp , [84] Takagi H., Queueing Analysis: A Foundation of Performance Evaluation, vol.2, Finite System, North-Holland, Amsterdam, [85] Takagi H., Explicit delay distribution in first-come first-served M/M/m/K and M/M/m/K/n queue and a mixed loss-delay system, Proceedings of Asia-Pacific Symposium on Queueing Theory and Its Applications to Telecommunication Networks, Korea, [86] Takine T., Hasegawa T., The workload in the MAP/G/l queue with state dependent services: Its application to a queue with preemptive resume priority', Comm. Statist. Stochastic Models, 10, pp , [87] Udagawa K., Nakamura G., "On a Queue in which Joining Customers Give up Their Services Halfway", J. Ops. Res. Japan 1, pp , [88] University of California at Los Engeles, Dept. of Engineering, An Engineering Analysis of Cargo Handling, Report 63-21,

9 [89] Wagner D., Analysis of mean values of a multi-server model with non-preemptive priorities and non-renewal input. Communications in Statistics, Stochastic Models. 13(1), pp , [90] Wagner D., Waiting time of a finite-capacity multi-server model with non-preemptive priorities, European Journal of Operational Research. 102, pp , [91] Wagner D., A finite-capacity multi-server multi-queueing model with non-renewal input. Annals of Operational Research. 79, pp , [92] Welch P. D., On preemptive resume priority queues, Ann. Math. Statist., 35, pp , [93] Wolf R. W., Poisson Arrivals See Time Averages, Opns. Res. 30, pp ,

I~EFERENCES. 2) Barrer, D.Y.(l957a). "Queueing with Impatient Customers and Indifferent Clerks." Oper. Res.5,

I~EFERENCES. 2) Barrer, D.Y.(l957a). Queueing with Impatient Customers and Indifferent Clerks. Oper. Res.5, I~EFERENCES I) Bailey, N.T.J.( 1952). "Study of Queues and Appointment Systems in Out-Patient Departments with Special Reference to Waiting Times." J.Roy. Statist Soc. Ser. B.l4, 185-199. 2) Barrer, D.Y.(l957a).

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