Queues with system disasters and impatient customers when system is down

  • Authors:
  • Uri Yechiali

  • Affiliations:
  • Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel 69978

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2007

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Abstract

Consider a system operating as an M/M/c queue, where c=1, 1cc=驴. The system as a whole suffers occasionally a disastrous breakdown, upon which all present customers (waiting and served) are cleared from the system and lost. A repair process then starts immediately. When the system is down, inoperative, and undergoing a repair process, new arrivals become impatient: each individual customer, upon arrival, activates a random-duration timer. If the timer expires before the system is repaired, the customer abandons the queue never to return. We analyze this model and derive various quality of service measures: mean sojourn time of a served customer; proportion of customers served; rate of lost customers due to disasters; and rate of abandonments due to impatience.