IJE TRANSACTIONS A: Basics Vol. 18, No. 1 (February 2005) 21-28   

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M. Jain and G.C. Sharma

Department of Mathematics, Institute of Basic Science
Khandari Campus, Dr. B.R. Ambedkar University
Agra-282002, India

Sharon Moses

Faculty of Mathematics, St. John’s College
Dr. B.R. Ambedkar University
Agra-282002, India

( Received: February 04, 2003 – Accepted: December 16, 2005 )

Abstract    This study deals with a state dependent machining system having provision of mixed spares. The service facility of the system consists of permanent as well as removable additional repairmen. When all the spares are utilized, the system works in short mode. The steady state solution of the queue size distribution is derived using product type solution. Expressions for some performance measures are established. Some earlier models are deduced as special cases of the model for specific values of the parameters.


Keywords    Machine repair, Queue, Mixed Spares, Removable Repairmen, State Dependent Rates, Queue Size



1. Sivazlian, B. D. and Wang, K. H., “Economic Analysis of the M/M/R Machine Repair Problem with Warm Standby”, Microelectron. Reliab, Vol. 29, (1989) 25-35.

2. Wang, K. H. and Sivazlian, B. D. “Cost Analysis of the M/M/R Machine Repair Problem with Spares Operating Under Variable Service Rates”, Microelectron. Reliab,, Vol. 32(8), (1992), 1171-1183.

3. Gupta, U. C. and Rao, S. T. S. S., “On the M/G/1 Machine Interference Model with Spares”, J. Perf. Eval., Vol. 24, (1996), 265-275.

4. Jain, M. and Dhyani, I., “Transient Analysis of M/M/C Machine Repair Problem with Spares”, G. C. Agra University J. Sci., Vol. 2, (1999), 16-42.

5. Jain, M. and Singh, C. J., “Finite Queuing Model with Random Failures and Delayed Repairs”, J. Agra Univ. Sci., Vol. 2, (1999), 8-13.

6. Shawky, A. I., “The Machine Interference Model M/M/C/K/N with Balking, Reneging and Spares”, Opsearch, Vol. 37(1), (2000), 25-35.

7. Jiang, X. Makis, V. and Jardine, A. K. S., “Optimal Repair/Replacement Policy for a General Repair Model”, Adv. Appl. Prob., Vol. 33, (2001), 206-222.

8. Grassmann, W. K., Chen, X. and Kashyap, B. R. K., “Optimal Service Rates for the State-Dependent M/G/1 Queue in Steady State”, Oper. Res. Letters, Vol. 29, (2001), 57-63.

9. Armstrong, M. J., “Age Repair Policies for the Machine Repair Problem”, J. Euro. Oper. Res., Vol. 138, (2002), 127-141.

10. Jain, M., “M/M/R Machine Repair Problem with Spares and Additional Repairmen”, Indian J. Pure Appl. Math., Vol. 29 (5), (1998), 517-524.

11. Jain, M., Singh, M. and Baghel, K. P. S., “M/M/C/K/N Machine Repair Problem with Balking, Reneging,

Spares and Additional Repairman”, J. GSR, Vol. 25-26, (2000a), 49-60

12. Jain, M. Singh, M. and Baghel, K. P. S., “Machine Repair Problem with Spares, Reneging, Additional Repairman and Two Modes of Failure”, J. MACT, Vol. 33, (2000b), 69-79.

13. Jain, M. and Sharma, G. C., “M/M/m/K Queue with Additional Servers and Discouragement”, IJE Trans. A., Vol. 15, No. 4, (2002), 349-354.

14. Jain, M. and Singh, P., “Performance Prediction of Loss and Delay Markoviam Queuing Model with Opposing and Removable Additional Servers”, Com. Oper. Res., Vol. 30, (2003), 1233-1253.

15. Keinrock, L., “Queuing Systems”, Vol. 1, John Wiley and Sons, New York, (1985).

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