Queues with system disasters and impatient customers when system is down

Consider a system (e.g. a computer farm or a call center) operating as a M/M/c queue, where c = 1, or 1 < c < ∞, or c = ∞. The system as a whole suffers disastrous breakdowns, resulting in the loss of all running and waiting sessions. When the system is down and undergoing a repair process, newly arriving customers become impatient: each individual customer activates a random-duration timer. If the timer expires before the system is repaired, the customer abandons the queue. 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. Keywords queues, M/M/1, M/M/c, M/M/∞, failures, disasters, impatience, abandonments, sojourn times, quality of service.

• Type: Journal
• Year: 2007
• Where: QUESTA
• Authors: Uri Yechiali
• Keywords: Customers, QUESTA 2007, Sojourn Times, Suffers Disastrous Breakdowns