b. N#25. Using the value of p found in (a), find the efficiency of slotted ALOHA by letting N approach infinity. Graph the efficiency of slotted ALOHA and pure ALOHA as a function of p for the following values of N: a. N#15. For a large number of users the ALOHA protocol is considered. c. N#35. There are two versions of ALOHA that is Pure ALOHA and Slotted ALOHA. a. Derive the value of p that maximizes the efficiency equation. Post Discussion. Hint: (1 – 1/N) N approaches 1/e as N approaches infinity. successful transmission S is: by single node: S= p (1-p)(N-1) by any of N nodes S = Prob (only one transmits)= N p (1-p)(N-1) 1 0 <> Discussions. This can reduce the efficiency of a network since colliding frames will cause loss of data in both the frames. Any station can transmit its data in any time slot. Aloha does not avoid hidden or exposed nodes and is generally inefficient in terms of usage of the channel: pure Aloha leads to a maximum efficiency of less than 1/(2e) ≈ 18.5%, compared to a single user system. Post the discussion to improve the above solution. In slotted ALOHA, the maximum efficiency is 36.8% when only one station transmits in one time slot . Please show the derivation. a) Recall that when there are N active nodes, the efficiency of slotted ALOHA is Np(1-p)^(N-1). If we find the derivative of this expression,… Engineering. Eytan Modiano Slide 10 Throughput of Slotted Aloha • The throughput is the fraction of slots that contain a successful transmission = P(success) = g(n)e-g(n) – When system is stable throughput must also equal the external arrival rate (λ) – What value of g(n) maximizes throughput? In Pure ALOHA no slotting was done but the efficiency was poor. The maximum efficiency of Pure Aloha is very less due to large number of collisions. Find the value of p that maximizes this expression. Find the value of p that maximizes this expression. Consider a slotted ALOHA system. The only condition is that station must start its transmission from the beginning of the time slot. Slotted Aloha- Slotted Aloha divides the time of shared channel into discrete intervals called as time slots. b. Slotted Aloha is an improvement to the original Aloha protocol, where discrete time slots were introduced to increase the maximum throughput while reducing collisions. My question is, if only one station is transmitting in one time slot, then there will be no collisions and since we are talking about maximum efficiency, all time slots will be utilized. https://www.cs.umd.edu/~shankar/417-F01/Slides/chapter5a-aus/sld022.htm 2. Tweet. (6 pts.) Slotted-Aloha type MAC protocols don't perform carrier sensing and synchronize the transmissions into time-slots. Suppose there are N active nodes sharing the channel. In Slotted ALOHA, slots have been made, so that every frame transmission starts at the beginning of the slot and throughput is increased by a factor of 2. Slotted Aloha efficiency limit of Nq*(1-q*)N nodes with many frames to send, each q (new arrival or re-Tx) used for useful probthat node 1 has success in a slot = q(1-q)N-1 Total expected utilization = Nq(1-q)N-1 For max efficiency with N nodes, find q* that maximizes Nq(1-q)N-1 For many nodes, take N-1 as N goes to infinity, gives 1/e = .37 exercises e-3 Aloha & Slotted Aloha efficiency Suppose N stations have packets to send meach transmits in slot with probability p mprob. P8. b. Answer. Recall that the efficiency is therefore Np(1-p)N-1, a. Slotted Aloha can utilize the channel up to nearly 1/e ≈ 37%. Recall that when there are N active nodes, the efficiency of slotted ALOHA is Np(1 – p) N–1 . Nodes sharing the channel in slot with probability p mprob the value of p in. 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