An M/G/1 Retrial Queue With Unreliable Server for Streaming Multimedia Applications

As a model for streaming multimedia applications, we study an unreliable retrial queue with infinite-capacity orbit and normal queue for which the retrial rate and the server repair rate are controllable. Customers join the retrial orbit if and only if their service is interrupted by a server failure. Interrupted customers do not rejoin the normal queue but repeatedly attempt to access the server at i.i.d. intervals until it is found functioning and idle. We provide stability conditions, queue length distributions, stochastic decomposition results, and performance measures. The joint optimization of the retrial and server repair rates is also studied. Now at Directorate of Force Management Policy; U.S. Air Force Headquarters, Manpower and Personnel. Corresponding author. Phone: (412) 624-9832. Now at The Boeing Company, Seattle, Washington. Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 2009 2. REPORT TYPE 3. DATES COVERED 00-00-2009 to 00-00-2009 4. TITLE AND SUBTITLE An M/G/1 Retrial Queue With Unreliable Server for Streaming Multimedia Applications 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Air Force Institute of Technology (AFIT/ENS),Department of Operational Sciences,2950 Hobson Way,Wright Patterson AFB,OH,45433-7765 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT As a model for streaming multimedia applications, we study an unreliable retrial queue with in?nite-capacity orbit and normal queue for which the retrial rate and the server repair rate are controllable. Customers join the retrial orbit if and only if their service is interrupted by a server failure. Interrupted customers do not rejoin the normal queue but repeatedly attempt to access the server at i.i.d. intervals until it is found functioning and idle. We provide stability conditions queue length distributions, stochastic decomposition results, and performance measures. The joint optimization of the retrial and server repair rates is also studied. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Same as Report (SAR) 18. NUMBER OF PAGES 25 19a. NAME OF RESPONSIBLE PERSON a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18