J. G. Dai and J. M. Harrison. The QNET method for two moment analysis of closed manufacturing systems. Ann. Appl. Probab., 3:968{ 1012, 1993. Home/Search Document Details and Download
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Control Problems in Telecommunications: The Heavy Traffic Approach - Kushner (2000) (Correct)
....capacity on the average) This operating regime is one of the crucial ones in applications, and e ective control is particularly important there. That the insights gained provide useful information even when in moderate trac is strongly suggested by numerous experiments in uncontrolled queues [16, 32, 70]. The methods exploit the fact that as the size of the system (e.g. number of sources and bandwidth) grows, with suitable scaling, central limit and law of large number type theorems come into play and allow important types of averaging or aggregation, which greatly simplify the analysis. It is ....
....limit or approximating equations can be solved analytically. But, most often, a numerical method must be used to solve the limit problem. If the problem is uncontrolled and the drift parameter and (nondegenerate) noise covariance of the limit problem are constant, then the so called QNET method [14, 15, 16, 17] has been an e ective numerical tool for estimating the stationary means and covariances of the queue length, even for high dimensional problems. The data in these references as well as in [55] or [65, 70] show that the heavy trac methods can often be used get very good estimates under conditions ....
J. G. Dai and J. M. Harrison. The QNET method for two moment analysis of closed manufacturing systems. Ann. Appl. Probab., 3:968{ 1012, 1993.
Reflecting Diffusions and Queueing Networks - Williams (1998) (Correct)
....multiplicative state space collapse holds for these two collections of networks. The qualifier Kelly type means that m k depends only on the station j at which class k is served, i.e. the limiting mean service times are station dependent, not classdependent quantities. In addition, it is known [DH93, Wi97b] that R is well defined and completely S for these networks. Combining the above results yields new heavy traffic limit theorems for these two collections of networks. In particular, the FIFO Kelly type network introduced by Dai, Wang and Wang (see Appendix A in [Wi97b] can be approximated by a ....
Dai, J. G., and Harrison, J. M. (1993). The QNET method for two-moment analysis of closed manufacturing systems. Ann. Appl. Prob., 3, 968--1012.
Existence and Uniqueness of Semimartingale Reflecting Brownian .. - Dai, Williams (1994) (28 citations) Self-citation (Dai) (Correct)
.... Harrison and Williams [23] Harrison [20] and Harrison and Nguyen [21, 22] For closed d station networks, the proposed approximating SRBM s live in the d dimensional simplex fx 2 IR d : x 1 : x d = 1g; see Harrison, Williams and Chen [24] Chen and Mandelbaum [9] Dai and Harrison [12]. Such an 6 ae ae ae ae ae ae ae ae= h h h h h h h h h h h h h h hhhhhhhhhhh Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi Delta Delta Delta Delta Delta Delta Delta Delta Delta Delta Gamma Gamma Gamma Gamma Gamma Gamma Gamma Gamma ....
Dai, J. G. and Harrison, J. M. The QNET method for two-moment analysis of closed manufacturing systems.. Annals of Applied Probability 3, 968--1012 (1993).
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