| M. Alanyali, B. Hajek (1996). On load balancing in Erlang networks, Stochastic Networks: Theory and Applications, F.P.Kelly, S.Zachary, I.Ziedens (Eds.), Oxford University Press. |
....given by 3 B(p) # 1 p#) Erl(c 1 ,# 1 p#) # 2 (1 p)#) Erl(c 2 ,# 2 (1 p)#) # 1 # 2 # , 1) where Erl(c, #) is the Erlang loss probability for a M M c c queue with arrival intensity # Erl(c, #) # c c # c i=0 # i i . The optimization problem is to find p # # [0, 1] that minimizes the average blocking probability B(p) This renders a unique solution due to the convexity of B(p) To see this, we use the fact that the expected loss rate given by #Erl(c, #) is an increasing and convex function of the arrival rate #, see [12] Intuitively this is clear since the ....
....the base station with the least relative load, defined for each base station k as the ratio of the number of channels occupied and the capacity i k c k ,k=1, 2. The switch curve in this case is given by s(i 1 ) c 2 c 1 i 1 . For the same model as discussed in this paper, Alanyali and Hajek [1] used fluid approximations to show that the LRR policy is asymptotically optimal in a heavy traffic setting. 10 11 12 13 14 15 1 1.2 1.4 1.6 1.8 2 (a) n 10 11 12 13 14 15 1 1.2 1.4 1.6 1.8 2 (b) l 1 ORR OFR GORR LRR FPI Figure 8: Comparisons of different policies for ....
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M. Alanyali, B. Hajek (1996). On load balancing in Erlang networks, Stochastic Networks: Theory and Applications, F.P.Kelly, S.Zachary, I.Ziedens (Eds.), Oxford University Press.
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Alanyali, M. and Hajek, B. (1996), "On Load Balancing in Erlang Networks", Stochastic Networks: Theory and Applications, F.P. Kelly, S. Zachary, and I. Ziedens (Eds.), Oxford University Press.
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