A queue with a pair of instantaneous independent bernoulli feedback processes

Abstract

In this paper we are concerned with several random processes that occur in M/G,/1 queue with instantaneous feedback in which the feedback decision process is a pair of independent Bernoulli processes. The stationary distribution of the output process has been obtained. Results for particular queues with feedback and without feedback are obtained. Some operating characteristics are derived for this queue. Some interesting results are obtained for departure processes. Optimum service rate is obtained. Numerical examples are provided to test the feasibility of the queueing model.

Sojourn times in queues with a pair of instantaneous independent bernoulli feedback

“…Figure 12 depicts the Sd (Sojourn time) versus service rate. When I = 11, f, = 0.6 and f, = 0.7, the standard deviation of sojourn time uniformly increases in the interval [5,10]. From Figure 10 service rate increases, Standard deviation of Sojourn time uniformly decreases.…”

“…The limiting distribution of the queue length of M/G/1 queue with Bernoulli feedback is equivalent to M / G / l queue without feedback [5]. But the limiting distribution of sojourn time of M / G / l queue with Bernoulli feedback is not equivalent to M/G/1 queue without feedback [ I ] .…”

“…We have studied various processes that occur in M/G2/1 queues with a pair of instantaneous Bernoulli feedback process [ 5 ] . In this paper, the stationary distributions for output and departure processes have been obtained.…”

The single server vacation queue with geometric abandonments and Bernoulli’s feedbacks

“…[3] have studied a single server queue with instantaneous Bernoulli's feedback and general service time distributions through Markov renewal process. Thangaraj and Santhakumaran [13] have studied a Markovian queue with instantaneous independent Bernoulli's feedback mechanism. Thangaraj and Santhakumaran [9] have analysed a queue with two types of delayed feedback.…”