QUEUES WITH STATE-DEPENDENT SERVICE TIMES

For a queue in which a (complete) service requires not only service to the customer about to be released from the queueing system but to all others in the queue as well, the (complete) service time will somehow depend on the queue length. A case of particular interest may be found in a stack of aircraft under the control of one air traffic controller. The first or bottom aircraft in the stack is released to the jurisdiction of another controller and all other aircraft in the stack are ordered, lowest aircraft first, to descend 1000 ft. No order may be issued to an aircraft until the aircraft beneath it has acknowledged commencing its descent. Hence, it is necessary, in principle at least, to perform some service for every customer in the stack before the secon air raft in the stack may be released to the jurisdiction of another controller. It would seem that, under the circumstances described, the expected service time or time between releases of successive aircraft should be proportional to the number of aircraft in the stack. This conclusion is substantiated by data analyses conducted by the Operations Research Group at Convair/Pomona (Smith et al., 1960) from which it was concluded that the average total duration of calls on radio-telephone communication facilities are essentially linear functions of the number of aircraft under control for all controller positions.

  • Corporate Authors:

    Transportation Research

    ,    
  • Authors:
    • ROSENSHINE, M
  • Publication Date: 1966-12

Subject/Index Terms

Filing Info

  • Accession Number: 00074402
  • Record Type: Publication
  • Source Agency: FLIGHT TRANSPORTATION LABORATORY, MIT DEPT. OF AERONAUTICS AND ASTRONAUTICS
  • Report/Paper Numbers: Vol 1
  • Files: TRIS
  • Created Date: Sep 5 1974 12:00AM