1. IEEE 802.11 Wireless LAN: Capacity Analysis and Protocol Enhancement F. Cali, M. Conti, E. Gregori IEEE 802.11 Wireless LAN: Capacity Analysis and Protocol Enhancement F. Cali, M. Conti, E. Gregori Vangelis Angelakis 23 / 3 / 2005 CS-539: Mobile Networks & Computing

2. Introduction CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Federico Cali, Marco Conti and Enrico Gregori "IEEE 802.11 Wireless LAN: Capacity Analysis and Protocol Enhancement" Proceedings of the Conference on Computer Communications IEEE Infocom’98 San Francisco, California, USA. March/April 1998. available online at: http://www.ieee-infocom.org/1998/papers/02a_2.pdf Institute for Informatics & Telematics (IIT), National Research Council (CNR), IT. Federico Cali, Marco Conti and Enrico Gregori "IEEE 802.11 Wireless LAN: Capacity Analysis and Protocol Enhancement" Proceedings of the Conference on Computer Communications IEEE Infocom’98 San Francisco, California, USA. March/April 1998. available online at: http://www.ieee-infocom.org/1998/papers/02a_2.pdf Institute for Informatics & Telematics (IIT), National Research Council (CNR), IT.

3. Introduction CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Communication in the 802.11 relies on a shared transmission medium. The 802.11 MAC layer coordinates the transmissions of the n/w STAs Transmission control information in the 802.11 MAC is both explicit and implicit. Explicit:Control Messages (ACK, RTS, CTS…) Implicit:Timing (SIFS, DIFS…) and Channel Condition (BUSY / IDLE –channel sensing ) Communication in the 802.11 relies on a shared transmission medium. The 802.11 MAC layer coordinates the transmissions of the n/w STAs Transmission control information in the 802.11 MAC is both explicit and implicit. Explicit:Control Messages (ACK, RTS, CTS…) Implicit:Timing (SIFS, DIFS…) and Channel Condition (BUSY / IDLE –channel sensing )

4. Introduction CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Control messages and message retransmissions reduce bandwidth available for successful message transmissions. The bandwidth fraction used for successfully transmitted messages gives a good indication of the overhead the MAC layer requires to perform its coordination task. Control messages and message retransmissions reduce bandwidth available for successful message transmissions. The bandwidth fraction used for successfully transmitted messages gives a good indication of the overhead the MAC layer requires to perform its coordination task.

5. Introduction CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Control messages and message retransmissions reduce bandwidth available for successful message transmissions. The bandwidth fraction used for successfully transmitted messages gives a good indication of the overhead the MAC layer requires to perform its coordination task. This is called Utilization and is usually influenced by several parameters. The paper focuses on: i) the number of active n/w STAs, and ii) the way they contribute to the offered load The maximum value of the Utilization is the MAC protocol Capacity Control messages and message retransmissions reduce bandwidth available for successful message transmissions. The bandwidth fraction used for successfully transmitted messages gives a good indication of the overhead the MAC layer requires to perform its coordination task. This is called Utilization and is usually influenced by several parameters. The paper focuses on: i) the number of active n/w STAs, and ii) the way they contribute to the offered load The maximum value of the Utilization is the MAC protocol Capacity

6. The 802.11 Medium Access Control CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 The basic access method in 802.11 MAC is the Distributed Coordination Function (DCF). The 802.11 DCF is a Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) MAC protocol. The basic access method in 802.11 MAC is the Distributed Coordination Function (DCF). The 802.11 DCF is a Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) MAC protocol.

7. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t

8. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C I have a packet to send to B, must sense the medium to avoid collissions t

9. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C Time passes… t DIFS

10. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t DIFS Channel idle for DIFS I am starting transmission to B. Channel idle for DIFS I am starting transmission to B.

11. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t τ DIFS

12. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t DIFS τ I have a packet to send… Sensed medium to be BUSY defering until IDLE I have a packet to send… Sensed medium to be BUSY defering until IDLE

13. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t DIFS τ deferring Must Acknowledge packet reception Must Acknowledge packet reception

14. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t DIFS τ Medium is IDLE, lets see if it remains idle for DIFS

15. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t DIFS τ Time passes… SIFS

16. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t DIFS τ SIFS deferring

17. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t DIFS τ SIFS Medium is IDLE, lets see if it remains idle for DIFS

18. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t DIFS τ Time passes… SIFS DIFS

19. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t DIFS τ Time passes… SIFS DIFS Backing off

20. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t DIFS τ SIFS DIFS Contention Window

21. 802.11 DCF CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B C C t DIFS τ SIFS DIFS Time slot = time required to sense the medium

22. Backoff handling CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 The # of slots (backoff interval) is uniformly selected in the (0, CW i ) interval With each idly passing slot the backoff timer is reduced If during the backoff interval the channel becomes busy then the timer is paused and is reactivated next time the channel is idle for DIFS If this leads to a collision, then the station will have to retransmit, this time selecting the backoff interval in the (0, 2 x CW i ) interval The initial CW is CWmin and a CWmax is also defined. The # of slots (backoff interval) is uniformly selected in the (0, CW i ) interval With each idly passing slot the backoff timer is reduced If during the backoff interval the channel becomes busy then the timer is paused and is reactivated next time the channel is idle for DIFS If this leads to a collision, then the station will have to retransmit, this time selecting the backoff interval in the (0, 2 x CW i ) interval The initial CW is CWmin and a CWmax is also defined.

23. RTS/CTS CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 The Request-To-Send / Clear-To-Send message exchange is optional. Used to avoid the hidden terminal problem. After gaining channel control and before the actual data packet transmission the sender sends a unicast RTS frame. This is answered by a broadcast CTS from the receiving STA. -The RTS/CTS mechanism is accounted for in this work. The Request-To-Send / Clear-To-Send message exchange is optional. Used to avoid the hidden terminal problem. After gaining channel control and before the actual data packet transmission the sender sends a unicast RTS frame. This is answered by a broadcast CTS from the receiving STA. -The RTS/CTS mechanism is accounted for in this work.

24. Capacity analysis: Definitions & Notations CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 ρ max the capacity in asymptotic conditions of M active stations ρ single the capacity considering a single active station asymptotic conditions (a.c.): All stations have a packet ready to transmit ideally: ρ single = ρ max = 1 The paper estimates capacity by evaluating in a.c. the ratio: _ Where: m average message length and t v virtual transmission time : the average time the channel is occpied in transmitting a message ρ max the capacity in asymptotic conditions of M active stations ρ single the capacity considering a single active station asymptotic conditions (a.c.): All stations have a packet ready to transmit ideally: ρ single = ρ max = 1 The paper estimates capacity by evaluating in a.c. the ratio: _ Where: m average message length and t v virtual transmission time : the average time the channel is occpied in transmitting a message

25. Capacity analysis: One active station CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Let S denote the time required for a successful transmission. Then assuming that the average backoff time is E [ CW ] it follows that: t v = E [ S ] + E [ CW ] We consider a single active station, no collisions => CW always from the (0, CWmin) interval => E [ CW ] = CWmin/2 LEMMA #1: Let S denote the time required for a successful transmission. Then assuming that the average backoff time is E [ CW ] it follows that: t v = E [ S ] + E [ CW ] We consider a single active station, no collisions => CW always from the (0, CWmin) interval => E [ CW ] = CWmin/2 LEMMA #1: (1) (2)

26. A short proof that CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B m Time: t 0

27. m A short proof that CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B Time: t 0 + m

28. m A short proof that CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B Time: t 0 + m + τ ab

29. ACK A short proof that CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B Time: t 0 + m + τ ab + SIFS

30. ACK A short proof that CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B Time: t 0 + m + τ ab + SIFS + τ ba

31. ACK A short proof that CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B Time: t 0 + m + τ ab + SIFS + τ ba + ACK

32. A short proof that CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 A A B B Time: t 0 + m + τ ab + SIFS + τ ba + ACK + DIFS

33. Capacity analysis: One active station CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 yields that E[S] = m + 2τ + SIFS + ACK + DIFS With (1), (2) & (3) it follows that Assuming packet lengths to be: - integer multiples of the slot length t slot - i.i.d. geometrically distributed with parameter q then yields that E[S] = m + 2τ + SIFS + ACK + DIFS With (1), (2) & (3) it follows that Assuming packet lengths to be: - integer multiples of the slot length t slot - i.i.d. geometrically distributed with parameter q then _ (3)

34. Capacity analysis: More active stations CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 In this case the virtual transmission time t v must include, not only the successful transmission, but also: -the collision intervals -the DIFS’ after each collision event -the propagation time τ -the idle periods due to the backoff algorithm In this case the virtual transmission time t v must include, not only the successful transmission, but also: -the collision intervals -the DIFS’ after each collision event -the propagation time τ -the idle periods due to the backoff algorithm Coll 1 DIFS Coll i DIFS S S … tv tv tv tv Idle_ p i Collision Successful transmission Successful transmission i i 1 1 Ν+1

35. Capacity analysis: More active stations CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 From the previous slide we have: In 802.11 duration of a collision equals the maximum length of the colliding packets. So, the collision duration ( Coll i ) depends on: - the packet size distribution - the backoff algorithm (number of colliding stations) The length of idle periods ( Idle_p i ) depends on - the backoff algorithm From the previous slide we have: In 802.11 duration of a collision equals the maximum length of the colliding packets. So, the collision duration ( Coll i ) depends on: - the packet size distribution - the backoff algorithm (number of colliding stations) The length of idle periods ( Idle_p i ) depends on - the backoff algorithm …

36. Capacity analysis: More active stations CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 To compute the two unknowns by taking the 802.11 backoff algorithm is impossible due to introduced interdependencies. Instead, the authors denote I to be the number of attempts to successfully transmit a packet. So each station experiences I backoff times {B 1, B 2, …, B I }, sampled uniformly in intervals of length {CW 1, CW 2,…,CW I } To compute the two unknowns by taking the 802.11 backoff algorithm is impossible due to introduced interdependencies. Instead, the authors denote I to be the number of attempts to successfully transmit a packet. So each station experiences I backoff times {B 1, B 2, …, B I }, sampled uniformly in intervals of length {CW 1, CW 2,…,CW I }

37. Capacity analysis: More active stations CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 To simplify the analysis authors assume that stations for each transmission attempt use a backoff interval sampled from a geometric distribution with parameter p, where p = 1 / ( E [B ] + 1 ), with E [B ] being the average value of {B 1, B 2, …, B I }, expressed in number of slots. LEMMA #2: E [B ] = (E [CW ] – 1) / 2 Where E [CW ] is the average contention window in number of slots. The above assumption on the backoff algorithm implies that future behaviour does not depend on the past. To simplify the analysis authors assume that stations for each transmission attempt use a backoff interval sampled from a geometric distribution with parameter p, where p = 1 / ( E [B ] + 1 ), with E [B ] being the average value of {B 1, B 2, …, B I }, expressed in number of slots. LEMMA #2: E [B ] = (E [CW ] – 1) / 2 Where E [CW ] is the average contention window in number of slots. The above assumption on the backoff algorithm implies that future behaviour does not depend on the past.

38. Capacity analysis: More active stations CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 So in a virtual transmission the following assumptions can be made (especially under a large number of stations M ): i)The idle periods duration Idle_p i are i.i.d. sampled from a geometric distribution with average E [ Idle_p ] ii)The collision duration Coll i are i.i.d. with average E [Coll ] So equation: Can become: So in a virtual transmission the following assumptions can be made (especially under a large number of stations M ): i)The idle periods duration Idle_p i are i.i.d. sampled from a geometric distribution with average E [ Idle_p ] ii)The collision duration Coll i are i.i.d. with average E [Coll ] So equation: Can become:

39. Capacity analysis: More active stations CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Shortly we will see how E [CW ] can be calculated and p derived from it Assuming it known, t v depends on E [N ], E [Idle_p ] and E [Coll ] LEMMA #3: If the backoff interval for each station is sampled for a geometric distribution with parameter p then: Shortly we will see how E [CW ] can be calculated and p derived from it Assuming it known, t v depends on E [N ], E [Idle_p ] and E [Coll ] LEMMA #3: If the backoff interval for each station is sampled for a geometric distribution with parameter p then:

40. Capacity analysis: Estimating E [ CW ] CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Lets focus on a tagged station and compute E [CW ] as the limiting value of the sequence {E [CW ( n ) ], n=1,2,…}. The first value of the sequence E [CW ( 0 ) ] is the average minimum CW and E [CW ( i+1 ) ] = Ψ (E [CW ( i ) ]) Specifically E [CW ( i+1 ) ] is the tagged station’s i- th average contention window computed under the assumption that all stations in the network transmit with probability p (i ) = 2 / ( E [CW ( i ) ]+1) Lets focus on a tagged station and compute E [CW ] as the limiting value of the sequence {E [CW ( n ) ], n=1,2,…}. The first value of the sequence E [CW ( 0 ) ] is the average minimum CW and E [CW ( i+1 ) ] = Ψ (E [CW ( i ) ]) Specifically E [CW ( i+1 ) ] is the tagged station’s i- th average contention window computed under the assumption that all stations in the network transmit with probability p (i ) = 2 / ( E [CW ( i ) ]+1)

41. Capacity analysis: Estimating Ψ (E [CW ( i ) ]) CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 When the tagged station transmits it will experience a collision if another station also attempts to transmit. The probability of a collision at the (i+1) -th attempt is p coll (i+1) = 1 – (1-p (i ) ) M-1 It follows that the tagged station will experience h collisions before successfully transmitting a packet with probabilty: P{N coll (i+1) =h } = ( p coll (i) ) h. (1 - p coll (i) ) Where N coll (i+1) is the number of collisions experienced by the tagged station at the (i+1) -th iteration When the tagged station transmits it will experience a collision if another station also attempts to transmit. The probability of a collision at the (i+1) -th attempt is p coll (i+1) = 1 – (1-p (i ) ) M-1 It follows that the tagged station will experience h collisions before successfully transmitting a packet with probabilty: P{N coll (i+1) =h } = ( p coll (i) ) h. (1 - p coll (i) ) Where N coll (i+1) is the number of collisions experienced by the tagged station at the (i+1) -th iteration

42. Capacity analysis: Estimating Ψ (E [CW ( i ) ]) CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Experiencing h collisions means that the station will use h +1 contention windows which will be selected according to the 802.11 backoff algorithm.

43. Capacity analysis: Estimating Ψ (E [CW ( i ) ]) CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Lemma #4: Denoting E h the set of contention windows used by the tagged station when it experiences h collisions before a successful transmission then: Where: and is given in the table  which is constructed considering the behaviour of the backoff algorithm Lemma #4: Denoting E h the set of contention windows used by the tagged station when it experiences h collisions before a successful transmission then: Where: and is given in the table  which is constructed considering the behaviour of the backoff algorithm

44. Simulation verification CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 The simulation confidence interval (confidence 90%) contains the analytically derived estimate Packets were assumed to have a geometric distribution with q =0.99. The simulation confidence interval (confidence 90%) contains the analytically derived estimate Packets were assumed to have a geometric distribution with q =0.99.

45. Backtracking CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 We had the following: We assume q, but needed p. We had p (i ) = 2 / ( E [CW ( i ) ]+1) And just showed the algorithm for E [CW ( i ) ] calculation. We had the following: We assume q, but needed p. We had p (i ) = 2 / ( E [CW ( i ) ]+1) And just showed the algorithm for E [CW ( i ) ] calculation.

46. The Capacity CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005

47. Capacity Bounds CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 For a given packet length, capacity is maximized when the average virtual transmission time is minimized. As we have seen t v is a function of M, p and q. Authors fix the values of q and M and try to derive the minimum of the t v ( p ) function. For a given packet length, capacity is maximized when the average virtual transmission time is minimized. As we have seen t v is a function of M, p and q. Authors fix the values of q and M and try to derive the minimum of the t v ( p ) function.

48. Capacity Bounds CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Low p values yield high t v values due to high number of empty slots before a transmission (low probability of collision) Low p values yield high t v values due to high number of empty slots before a transmission (low probability of collision) High p values imply a high number of collisions before a successful transmission. Bottom line: The minimum t v can be derived for each q and from that the analytical upper bound of the MAC capacity. High p values imply a high number of collisions before a successful transmission. Bottom line: The minimum t v can be derived for each q and from that the analytical upper bound of the MAC capacity.

49. Capacity Bounds CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005

50. Improving the IEEE 802.11 MAC capacity CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 The critical point for the distance between the analytical capacity bound and the simulated results is the average backoff time which determines the probability of a collision: p (i ) = 2 / ( E [CW ( i ) ]+1) To demonstrate the figure compares the analytical bound to a simulation of an 802.11 network with a constant contention window sized equal to the optimal value 2/p min -1 with the value of p min taken from the table in the previous slide. To demonstrate the figure compares the analytical bound to a simulation of an 802.11 network with a constant contention window sized equal to the optimal value 2/p min -1 with the value of p min taken from the table in the previous slide.

51. Improving the IEEE 802.11 MAC capacity CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Goal: to reach the analytically estimated capacity bound Method: modify the 802.11 backoff algorithm, providing it with an optimal constant CW. Bummer: optimal CW is derived from the p min and the p min value depends also on M and q. i.e.: the optimal CW size depends on the network load… To reach the maximum capacity the contention window must be computed in real-time estimating the M and q values… Goal: to reach the analytically estimated capacity bound Method: modify the 802.11 backoff algorithm, providing it with an optimal constant CW. Bummer: optimal CW is derived from the p min and the p min value depends also on M and q. i.e.: the optimal CW size depends on the network load… To reach the maximum capacity the contention window must be computed in real-time estimating the M and q values…

52. Capacity with known M CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 In theory, observing the channel status, a station can estimate the average collision length and the average number of collisions and with a minimization algorithm obtain p min. Authors argue that it is unsuitable for run-time and propose a heuristic for the estimation of p min. Remember: i) values of p lesser than p min correspond to the case in which E [Idle_p] dominates the t v. ii) values of p greater than p min correspond to the case in which collisions dominate the t v. In theory, observing the channel status, a station can estimate the average collision length and the average number of collisions and with a minimization algorithm obtain p min. Authors argue that it is unsuitable for run-time and propose a heuristic for the estimation of p min. Remember: i) values of p lesser than p min correspond to the case in which E [Idle_p] dominates the t v. ii) values of p greater than p min correspond to the case in which collisions dominate the t v.

53. p min approximation CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 With this in mind p min is close enough to a p value that satisfies: E [Coll ]. E [N c ] = (E [N c ] + 1). E [Idle_p ]. t slot Simplification: for p close to p min the number of collisions is stationary and so E [Coll ] can be taken to be constant. So with With this in mind p min is close enough to a p value that satisfies: E [Coll ]. E [N c ] = (E [N c ] + 1). E [Idle_p ]. t slot Simplification: for p close to p min the number of collisions is stationary and so E [Coll ] can be taken to be constant. So with

54. p min estimation CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005

55. 802.11 + CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Each station start with CW set to the standard CWmin. (authors use the legacy 802.11 draft specs. with CWmin=32) CW is updated at the end of each t v which contains at least one collision Each station runs the algorithm to estimate p min, and the estimate of the contention window is now 2 / (p min –1) With this the current CW is updated as: CW = a. CW + (1-a). (2 / (p min –1)) a having the role of a smoothing factor. Each station start with CW set to the standard CWmin. (authors use the legacy 802.11 draft specs. with CWmin=32) CW is updated at the end of each t v which contains at least one collision Each station runs the algorithm to estimate p min, and the estimate of the contention window is now 2 / (p min –1) With this the current CW is updated as: CW = a. CW + (1-a). (2 / (p min –1)) a having the role of a smoothing factor.

56. 802.11 + capacity CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005

57. M unknown CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 Assume a wrong idea for the number active stations…

58. Run-time M estimation CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005 From lemma 3, equations denoting Total_Idle_p the average number of empty slots, we derive: and so: From lemma 3, equations denoting Total_Idle_p the average number of empty slots, we derive: and so:

59. Result of estimating M CS-539 Mobile Networks & Computing Vangelis Angelakis 23/3/2005