On queueing with customer impatience until the end of service

Abstract

We study queueing systems where customers have strict deadlines until the end of their service. An analytic method is given for the analysis of a class of such queues, namely, M(n)/M/1 + G models with ordered service. These are single-server queues with state-dependent Poisson arrival process, exponential service times, FCFS service discipline, and general customer impatience. We derive a closed-form solution for the conditional probability density function of the offered sojourn time, given the number of customers in the system. This is a novel result that has not been known before. Using this result, we show how the probability measure induced by the offered sojourn time is computed, and consequently how performance measures such as the probability of missing deadline and the probability of blocking are obtained. This is further illustrated through a numerical example.

An overhead and resource contention aware analytical model for overloaded Web servers

“…From Table 1, we see that the two models that come closest to our requirements are those by Movaghar (2000Movaghar ( , 1996 and Pla et al (2004).…”

“…There is significant amount of literature that studies the behavior of queuing systems along the various aspects that we outlined earlier (Reeser and Hariharan, 2002;Chen and Mohapatra, 2003;Dalal and Jordan, 2001;Doshi and Heffes, 1986;Movaghar, 1996;Movaghar, 2000;Pla et al, 2004). In order to compare the existing work in a structured manner, we characterize the work according to the following features: whether the model is simulation based or analytical, the timeout distribution assumed, the removal policy on timeout, the number of servers, the buffer size, whether resource sharing has been considered and the scheduling policies considered.…”

“…More recently, Pla et al (2004) and Movaghar (1996Movaghar ( , 2000 have studied and solved models that involve queuing with impatient customers. As can be seen from Table 1, these models are quite general, and capture most of the characteristics that we require.…”

“…Movaghar's work provides us with analysis for queues with impatient customers with deadlines until beginning of service (Movaghar, 1996) and till the end of service (Movaghar, 2000), with FIFO queuing discipline. Thus, using our notation, Movaghar gives us results for the M/M/C/K/FIFO + G/BUF and the M/M/C/K/FIF-O + G/ANY queuing models.…”

“…Thus the basic models are unable to reproduce the degradation of goodput in an overloaded condition. More sophisticated models such as the ones by Pla et al (2004) and Movaghar (1996Movaghar ( , 2000 do account for abandonment-however, they are still unable to explain the phenomenon of drastic degradation of goodput of the server.…”