Fluid limits for overloaded multiclass FIFO single-server queues with general abandonment
We consider an overloaded multiclass nonidling first-in-first-outsingle-server queue with abandonment. The interarrival times, servicetimes, and deadline times are sequences of independent and identically,but generally distributed random variables. In prior work, Jennings andReed studied the workloa...
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| Format: | Article |
| Language: | English |
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Institute for Operations Research and the Management Sciences (INFORMS)
2013-01-01
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| Series: | Stochastic Systems |
| Subjects: | |
| Online Access: | http://www.i-journals.org/ssy/viewarticle.php?id=85&layout=abstract |
| _version_ | 1811239663500787712 |
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| author | Amber L. Puha Otis B. Jennings |
| author_facet | Amber L. Puha Otis B. Jennings |
| author_sort | Amber L. Puha |
| collection | DOAJ |
| description | We consider an overloaded multiclass nonidling first-in-first-outsingle-server queue with abandonment. The interarrival times, servicetimes, and deadline times are sequences of independent and identically,but generally distributed random variables. In prior work, Jennings andReed studied the workload process associated with this queue. Undermild conditions, they establish both a functional law of large numbersand a functional central limit theorem for this process. We build on thatwork here. For this, we consider a more detailed description of thesystem state given by <i>K</i> finite, nonnegative Borel measures on thenonnegative quadrant, one for each job class. For each time and jobclass, the associated measure has a unit atom associated with each jobof that class in the system at the coordinates determined by what arereferred to as the residual virtual sojourn time and residual patiencetime of that job. Under mild conditions, we prove a functional law oflarge numbers for this measure-valued state descriptor. This yieldsapproximations for related processes such as the queue lengths andabandoning queue lengths. An interesting characteristic of theseapproximations is that they depend on the deadline distributions intheir entirety. |
| first_indexed | 2024-04-12T13:05:06Z |
| format | Article |
| id | doaj.art-bfa8d9ea0c6946ba88f76aa1f0a9f220 |
| institution | Directory Open Access Journal |
| issn | 1946-5238 |
| language | English |
| last_indexed | 2024-04-12T13:05:06Z |
| publishDate | 2013-01-01 |
| publisher | Institute for Operations Research and the Management Sciences (INFORMS) |
| record_format | Article |
| series | Stochastic Systems |
| spelling | doaj.art-bfa8d9ea0c6946ba88f76aa1f0a9f2202022-12-22T03:32:04ZengInstitute for Operations Research and the Management Sciences (INFORMS)Stochastic Systems1946-52382013-01-0131262321Fluid limits for overloaded multiclass FIFO single-server queues with general abandonmentAmber L. PuhaOtis B. JenningsWe consider an overloaded multiclass nonidling first-in-first-outsingle-server queue with abandonment. The interarrival times, servicetimes, and deadline times are sequences of independent and identically,but generally distributed random variables. In prior work, Jennings andReed studied the workload process associated with this queue. Undermild conditions, they establish both a functional law of large numbersand a functional central limit theorem for this process. We build on thatwork here. For this, we consider a more detailed description of thesystem state given by <i>K</i> finite, nonnegative Borel measures on thenonnegative quadrant, one for each job class. For each time and jobclass, the associated measure has a unit atom associated with each jobof that class in the system at the coordinates determined by what arereferred to as the residual virtual sojourn time and residual patiencetime of that job. Under mild conditions, we prove a functional law oflarge numbers for this measure-valued state descriptor. This yieldsapproximations for related processes such as the queue lengths andabandoning queue lengths. An interesting characteristic of theseapproximations is that they depend on the deadline distributions intheir entirety.http://www.i-journals.org/ssy/viewarticle.php?id=85&layout=abstractOverloaded queueabandonmentfirst-in-first-outmulticlass queuemeasure-valued state descriptorqueue-length vectorfluid limitsfluid modelinvariant states |
| spellingShingle | Amber L. Puha Otis B. Jennings Fluid limits for overloaded multiclass FIFO single-server queues with general abandonment Stochastic Systems Overloaded queue abandonment first-in-first-out multiclass queue measure-valued state descriptor queue-length vector fluid limits fluid model invariant states |
| title | Fluid limits for overloaded multiclass FIFO single-server queues with general abandonment |
| title_full | Fluid limits for overloaded multiclass FIFO single-server queues with general abandonment |
| title_fullStr | Fluid limits for overloaded multiclass FIFO single-server queues with general abandonment |
| title_full_unstemmed | Fluid limits for overloaded multiclass FIFO single-server queues with general abandonment |
| title_short | Fluid limits for overloaded multiclass FIFO single-server queues with general abandonment |
| title_sort | fluid limits for overloaded multiclass fifo single server queues with general abandonment |
| topic | Overloaded queue abandonment first-in-first-out multiclass queue measure-valued state descriptor queue-length vector fluid limits fluid model invariant states |
| url | http://www.i-journals.org/ssy/viewarticle.php?id=85&layout=abstract |
| work_keys_str_mv | AT amberlpuha fluidlimitsforoverloadedmulticlassfifosingleserverqueueswithgeneralabandonment AT otisbjennings fluidlimitsforoverloadedmulticlassfifosingleserverqueueswithgeneralabandonment |