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Analysis of IEEE 802.16 Mesh Mode Scheduler Performance

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### Analysis of IEEE 802.16 Mesh Mode Scheduler Performance

Outline

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 4, APRIL 2007

Min Cao, Wenchao Ma, Member , IEEE, Qian Zhang, Senior Member , IEEE,

and Xiaodong Wang, Senior Member , IEEE

Presentd by Chan Chih-Yuan (詹志元）

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Author (1/4)

Min Cao

- Currently he is a Ph.D. candidate in the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign.
- His research interest include mobile computing and distributed systems, performance analysis and wireless networks.

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Author (2/4)

Wenchao Ma

- Received the Ph.D. degree from the University of Florida, Gainesville, in 2003.
- He also worked with Microsoft Research Asia before 2005 as an associate researcher and currently works with Lenovo Corporate Research and Development as researcher staff.
- His research interests include wireless multimedia networks, mobility management, mobile computing, mobile IP, P2P technology and broadband wireless access.

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Author (3/4)

Qian Zhang

- Received Ph.D. degrees from Wuhan University, China. Dr. Zhang joined the Hong Kong University of Science and Technology in Sept. 2005 as an Associate Professor.
- Her current research interests are in the areas of wireless communications, IP networking, multimedia, P2P overlay, and wireless security.
- Dr. Zhang is an Associate Editor for the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY,and Computer Networks.

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Author (4/4)

Xiaodong Wang

- received the Ph.D degree from Princeton University, all in Electrical Engineering. Since January 2002, he has been with the Department of Electrical Engineering, Columbia University
- His current research interests include wireless communications, statistical signal processing, and genomic signal processing.
- He currently serves as an Associate Editor for the IEEE TRANSACTIONS ON COMMUNICATIONS,the IEEE TRANSACTIONS ON WIRELESSCOMMUNICATIONS, the IEEE TRANSACTIONS ON SIGNAL PROCESSING, the IEEE TRANSACTIONS ON INFORMATION THEORY.

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Outline

- Introduction
- IEEE 802.16 Distributed Scheduling
- Performance Analysis
- Evaluation
- Conclusion

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Introduction (1/4)

- In order to improve network coverage and scalability, mesh mode is supported in Wireless MAN.
- In the mesh mode, the nodes are organized in an ad-hoc fashion, and all nodes are peers can act as routers to relay packets for their neighbors.
- A node can choose the links with the best quality to transfer; and with an intelligent routing protocol, the traffic can be routed to avoid the congested area.

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Introduction (2/4)

- Although the mesh mode exhibits better flexibility and scalability, the distributed channel access control is more complex because every node compute its transmission time without global information.
- In distributed scheduling, every node competes for channel access using a pseudo-random election algorithm based on the scheduling information of the two-hop neighbors, and data subframes are allocated through a request-grant-confirrm three-way handshaking procedure.

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Introduction (3/4)

- It is necessary to understand the distributed scheduler behavior thoroughly to optimize the network throughput and delay performance. In this paper, we focus on the performance of the distributed scheduling algorithm.
- The IEEE 802.11 DCF (distributed coordination function) also supports ad hoc mode. However, these performance analysis approaches for the IEEE 802.11 cannot be applied to the IEEE 802.16 mesh mode because the two protocols differ in many fundamental aspects.

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Introduction (4/4)

- Particularly, we develop a stochastic model to analyze the control channel performance.
- This model considers the important parameters that could affect the system performance like the total node number, holdoff exponent value, and topology.
- With this model, the channel contention situation and connection setup time variance can be evaluated clearly under different parameters.

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IEEE 802.16 Distributed Scheduling

- The transmission opportunity and minislot are the basic unit for resource allocation in the control and data subframes respectively.

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In IEEE 802.16 mesh mode, the channel access in the control subframe is coordinated in a distributed manner mong two-hop neighbors, and the data subframe slot allocation is performed through the control message exchange so that there is no contention in the data subframe.

- Each node competes for transmission opportunities in the control subframe based on its neighbors’ scheduling information such that in a two-hop neighborhood, only one node can broadcast its control message at any time.

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Once a node wins the control channel, a range of consecutive transmission opportunities are allocated to this node, which is called an eligible interval and the node can transmit in any slot in the interval. Every node needs to determine its next eligible interval during the current one.

- A pseudo-random function based distributed election algorithmdefined in the standard is used to decide whether the node winsa candidate transportation opportunity.
- If it wins, the reservation information is broadcast to the neighbors, otherwise the next slot is selected as a candidate and the procedure repeats until the node wins.

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By broadcasting the MSH-DSCH (Mesh Mode Distributed Scheduling) messages, each node can have the scheduling information of its two-hop neighbors.

- In the MSH-DSCH message, two parametersare included for control channel scheduling - Next_Xmt_Mxand Xmt_Holdooff_Exponent.
- The first parameter indicates the sequence number of the first slot in the eligible interval and the eligible length is L = 2Xmt_Holdoff_Exponent transmission opportunities. The holdoff exponent value can decide a node channel contention frequency and affect all the nodes in two-hop neighborhood.

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In order to solve the contention, the standard defines a pseudo-random function with the slot sequence number and all IDs of the competing nodes as inputs.

- The output values are called mixing values. If the current node ID and the slot number generate the largest mixing value, it wins this slot and broadcasts the new schedule to the neighbors.
- If the node fails, the next transmission opportunity is set to be the temporary transmission slot and the above competing procedure is repeated until it wins in a slot.

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Outline

- Introduction
- IEEE 802.16 Distributed Scheduling
- Performance Analysis
- Evaluation
- Conclusion

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PERFORMANCE ANALYSIS

A. Model and Approach

- The control subframe is independent of the data subframe. We consider the modeling and analysis of the control subchannel, which is characterized by the distributed election algorithm.
- Assume that the number of nodes in the network is N.Let denote the set of 2-hops neighbor nodes of node k, denote the set of nodes whose the schedules are unknown in the neighbor nodes set .

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Let denote the holdoff exponent of node k, then is the holdoff time of node k.is the eligibility interval of node k.

- Let denote the number of slots that node k fails before it wins the first slot with the pseudo-random competition, which is a random variable, then the interval between successive transmission opportunities is .
- Let denote the number of transmissiontimes of node k up to slot t, then is a counting process with interevent time .

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To simplify the analysis, we make the following assumptions:

- (1)the counting process of each node eventually reaches its steady state and the intervals are i.i.d., that is, , forms a stationary and ergodic renewal process.
- (2)the renewal processes of different nodes are mutually independent at their steady states.

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Note that the distribution of the renewal intervals of each node depends on the number of competing nodes in its neighborhood and their holdoff exponent.

- Our analysis is based on the above assumptions.

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Suppose that the expected number of competing nodes in slot s for the node k is .

- As a result of the pseudo-random election algorithm, the probability that this node wins the slot is
- So the probability mass function of is

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To get the distribution of , we need to find . But depends on the distributions of since all the nodes in the neighborhood of node k are candidates to compete with node k.

- the following approach to solve this problem: derive in terms of by modelling the distributed election algorithm, and then by using the relation we obtain a set of close form equations for to solve them

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B. Collocated Scenario

1) Identical Holdoff Exponents:

- we first assume equal holdoff exponents, i.e., . Hence when the nodes are collocated, the transmission interval has the same distribution,
- Let be a renewal process ant t be any chosen time slot, the spread, is the renewal interval in which t lies.

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Renewal Process

- A renewal process is a generalisation of the Poisson process. In the same informal spirit, we may define a renewal process to be the same thing, except that the holding times take on a more general distribution.

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The limiting distribution of excess time is established by the following lemma, which is a corollary of the Renewal Reward Theorem.The proof is similar to that for the continuous-time version of the lemma in [20]

- The limiting distribution of the excess time is for fixedwhere and is an indicator function.

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By the stationary and ergodic assumption, we can take the limiting distribution of excess time as its stationary distribution

- The distribution of τ is given in terms of {p(s)} aswhere

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Since the renewal process of node k and node j are assumed to be statistically independent, at the current transmit time t of node k, the time from t to the next transmit time of node j is simply the excess time of node j.

- By the assumption that the renewal process is stationary and that the distributions of are identical, we can simply denote as e.

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When the holdoff exponents of all the nodes are identical this probabilities is the same for any two nodes k and j.

- By the assumption of statistical independence
- Hence the expected number of nodes competing with node k in slot s is and the competing nodes in slot s for node k is
- Substituting (9) into (1) we get

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Combining (8) and (10), we get a set of equations by which we can solve for p(s), s=1,2,.... Typically, as , so we can truncate the tail and consider only p(s), s=1,2,…,L for some large L, and then solve the fixed point equations by using standard iterative method.

- By observing the histograms of our simulation, we find that the distribution of S can be approximated by a geometric distribution. So we make a further approximation that

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Then we have similar to (4) and (5) we can derive the distribution of as followsand the distribution of as

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Then the probability that another node j will compete with node k in the given slot is

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For the geometric distribution, for all s, hence for all s, which implies that the number of competing nodes in each slot s should be the same. Here we approximate M asthe expectation of as

- Using (14) and (15) and after some manipulations, we get

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By observing the histograms of our simulation data, we find that the distribution of S can be approximated by a geometric distribution. So we make a further approximation that

- Then we have . Similar to (4) and (5) we can derive the distribution of τ as follows

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The distribution of as

- Then the probability that another node will compete with node k in the given slot is

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Substitute , and into (17), we express the above equation in terms of as

- A fixed point iteration can be used to obtain E[S] from (18).

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2) Nonidentical Holdoff Exponents:

Now we consider the case where holdoff exponents is not identical.

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Denote as the probability that node j will compete with node k in the given slot , which is given by (21), where .

- Again, by the assumption of statistical independence,

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Similarly we can find the distributions ofby the fixed point iterations. We further assume that are geometrical distributed as before, that is, assume

- Hence the distribution of is

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To estimate , we proceed as follows

- Derive from (21), (23) and (25). Here we directly give the approximation result as

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Note that combining (26) and (27), we have

- Again we can solve for using fixed point iteration.

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3) General Topology Scenario:

- (1)the neighborhood node sets of different nodesmay be different
- (2)there exist unknown nodes, hence besides the competing cases 1 and 2, there are unknown competing nodes.
- Since unknown nodes are always regarded as competing nodes in each slot by the distributed election algorithm, we have

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D. Performance Metrics Estimation:

- Let denotes the time node A needs to accomplish a three-way handshaking with node B.
- Now we can derive given the distributions of of all nodes
- is the time interval between node A sending a Request to B and B replying a Grant to A. is the time interval between B sending the Grant and A replying with a Confirm.

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By the independence assumption, and further assuming that the renewal processes of node A and B have run for a long time so that we can assume that follows a limiting distribution as the excess time

- However, may not follow the same distribution as since it is dependent on , thus the limiting distribution doesnot hold.It is very complicated to find the exactdistribution ofsince the renewal interval is not geometrical distributed.

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Note that when , the renewal process of node A can be considered to run for a long time after sending Request, so in this case we can assume that

- In this case,
- On the other hand, when , since the portion of excess time is negligible, and

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- Empirically, estimated as
- Based on the simulation data, we find for the identical holdoff exponents case and for the nonidentical exponents case.

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Once is known, from (25) we can calculate

- Employing the results of from previous subsections, we can determine for any two neighbor nodes handshake A and B by using (32) and (33).

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Outline

- Introduction
- IEEE 802.16 Distributed Scheduling
- Performance Analysis
- Evaluation
- Conclusion

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Evaluation

- A. Simulation Methodology

1) Collocated Scenario:

- The total transmission opportunities in control channel becomes 256 when the exponent value is 4.
- Varying the total node number from 10 to 128 to study the scheduler performance

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2) General Topology:

- The scheduling information of some neighbors beyond one hop may become stale.
- The reason is that some one-hop neighbors could not update the schedule information in time for some specific transmission order.
- A neighbor node becomes unknown node once is schedule information is stale and always be treated as potential competitor.

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B. Numerical Results

(1) Transmission Interval:

- In the identical case:
- The node transmission intervals increase with the total node number and exponent values.
- When N becomes larger, the contention becomes more intensive so that a node has to compete more times before wins.

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In the nonidentical exponent case:

- Divding the N nodes into five group of equal size. The nodes in each group takes the same exponent value from the set {0,1,2,3,4}.
- The analytical and simulation results are also compared. The system behaves similarly as in the identical exponent scenario with longer transmission intervals.

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(2) Three-Way Handshaking Time: (2/2)

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(3) General Topology Scenario:

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- Introduction
- IEEE 802.16 Distributed Scheduling
- Performance Analysis
- Evaluation
- Conclusion

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CONCLUSIONS (1/2)

- In the mesh mode, every node competes for the channel access in a distributed manner and tries to broadcast its scheduling information periodically.
- This model assumes that the transmit time sequences of all the nodes in the control subframe form statically independent renewal processes.

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CONCLUSIONS (2/2)

- A good reservation scheme should guarantee the bandwidth allocation fairness and improve the channel utilization at the same time.
- Such a reservation scheme needs the information such as the connection setup time and contention success probability provided by this model.
- Our future work is to propose such a reservation scheme taking into account the tradeoff between system resource utilization and the connection QoS requirement.

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In our study, we assumes the transmit time sequences of all the nodes in the control subframe form statistically independent renewal processes.

- Based on this assumption, we develop a stochastic model to estimate the control channel performance.

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