throbber
I Umted States Patent [19]
`Angelico et a1.
`
`US005706274A
`[11] Patent Number:
`[45] Date of Patent:
`
`5,706,274
`Jan. 6, 1998
`
`[S4] CSMA WITH DYNAMIC PERSISTENCE
`
`6/1994 Ftidrich et a1. ...................... .. 370/853
`5,319,641
`5,369,639 11/1994 Kamerman et a1.
`. 370/853
`
`
`
`Inventors: Dean A‘ Angelico‘ Pleasanton; James A. Hayes. San Jose. both of Calif.
`
`[73] Assignee: Tetherless Access Ltd- (TAL).
`Sunnyvale. Calif.
`
`,
`[21] Appl' No" 525x59
`[22] Filed:
`Sep. 7, 1995
`
`[51] Int. Cl.6 ................................................. .. H04L 12/413
`[52]
`Cl.
`370,853
`[58] Field of Search
`370/85 3 85 2
`5'8‘25 d5‘
`'
`‘ 825' of;
`'
`
`'
`
`‘
`
`‘
`
`’
`
`‘
`
`’
`
`
`
`8t OTHER PUBLICATIONS .......................... n
`
`
`
`Level Protocols Revisit
`
`Phil Karn et 31.. 1987.
`
`Primary Examiner--Douglas W. Olms
`Assistant Examiner-Chau T. Nguyen
`Attorney Agent, or Firm-Townsend and Townsend and
`Crew LLP
`
`ABSTRACT
`[57]
`A method and apparatus for dynamically determining the
`persistence value P at a node in a P-persistent CSMA
`wireless network by determm' ing the number of nodes to
`which the given node has an established link and which have
`transmitted within a preceding period of time is provided
`The preceding period of time is between 5-60 seconds.
`preferably approximately 10 seconds. The value of P is set
`to a value between 1/(0.5N+1) and l/(2N+l), preferably
`appmmtcly 1’ (M1)"
`
`18 Claim‘ 5, 4 Drawm' g Sheets
`
`[56]
`
`.
`Refemnces Clwd
`U.S. PATENT DOCUMENTS
`370,852
`4506361 3/1985
`.. 370/853
`4,979,168 12/1990 Courtois et al.
`370/853
`5,042,083
`8/1991 Ichikawa ....... ..
`5,175,537 12/1992 Jalfe et al. ........................... .. 370/853
`
`RECEIVE DATA
`PACKET FOR
`TRANSMISSION
`
`E
`
`WAIT FOR
`END OF ANY
`TRANSMISSION /F
`ON CHANNEL
`
`1
`
`GOTO
`G
`DETERMINE
`N ROUTINE /
`
`GENERATE
`I
`RANDOM NO.
`o < R < 1 /
`
`J
`
`N0
`
`YES
`
`[K
`
`TRANSMIT
`
`[ L
`
`WAIT
`SLOT TIME
`
`DETECT
`TRANSM ISSION
`
`FIG. 7
`
`Petitioners' Ex. 1015 - Page 1
`
`

`
`US. Patent
`
`Jan. 6, 1998
`
`Sheet 1 of 4
`
`5,706,274
`
`18
`
`External ontenno
`(omnidirectional or directional)
`
`l
`
`I
`
`'
`
`Customer's LAN
`FIG. .1
`
`Backbone site
`
`Customers
`
`l Q <1
`YWII:
`
`L_________
`
`Petitioners' Ex. 1015 - Page 2
`
`

`
`US. Patent
`
`Jan. 6, 1998
`
`Sheet 2 of 4
`
`5,706,274
`
`[20
`
`25
`25 External antennae
`(omnidirectional or direciionul)
`26
`25
`
`Trunk network:
`Wireline, microwave,
`high-speed spread
`25 spectrum radio, or
`satellite
`
`_TAL
`wnretless
`T0“ N5
`24
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`g 24
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`I
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`a
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`I
`
`a
`24
`
`Trunk network A
`
`FIG. 3
`
`Petitioners' Ex. 1015 - Page 3
`
`

`
`US. Patent
`
`Jan. 6, 1998
`
`Sheet 3 of 4
`
`TRANSMITTER
`
`RECEIVER
`
`lll'llll-llilll.
`
`FIG. 4
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`
`5
`
`Petitioners' Ex. 1015 - Page 4
`
`

`
`US. Patent
`
`Jan. 6, 1998
`
`Sheet 4 0f 4
`
`5,706,274
`
`RECEIVE DATA
`PACKET FOR
`TRANSMISSION
`
`/E
`
`WAIT FOR
`END OF ANY
`TRANSMISSION
`ON CHANNEL
`
`GOTO
`DETERMINE
`N ROUTINE
`
`GENERATE
`RANDOM NO.
`
`0 < R < 1 /-I
`
`J
`
`NO
`
`YES
`
`K
`
`/
`
`TRANSMIT
`
`WAIT
`SLOT TIME
`
`DETECT
`TRANSMISSION
`
`FIG. 7
`
`Petitioners' Ex. 1015 - Page 5
`
`

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`5,706,274
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`15
`
`25
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`2
`The present invention is directed in particular to the ?eld
`of wireless. or radio transmission. networks. Such networks
`are particularly useful where there is not an infrastructure of
`wired lines to allow interconnection of networks. Awireless
`network has particular issues that are not involved in a wired
`local area network. One issue is the dilference in transmis
`sion power of the various nodes and the possibility for
`interference. such that it is possible that not all nodes can
`hear each other. depending upon the distance and geographi
`cal interference. In addition, it is possible for a ?rst node to
`hear a second node. but not vice versa. Another unique
`feature of wireless networks is that collision detection is
`very di?icult. due to the fact that any radio receiver inte
`grated with a transmitter would hear only its local
`transmitter. not a remote one.
`
`SUMMARY OF THE INVENTION
`
`The present invention provides a method and apparatus
`for dynamically determining the persistence value P at a
`node in a wireless network by determining the number of
`nodes to which the given node has an established link and
`which have transmitted within a preceding period of time.
`The preceding period of time is between 5-60 seconds.
`preferably approximately 10 seconds. The value of P is set
`to a value between 1/(0.5N+1) and l/(2N+1). preferably
`approximately 1/(N+l).
`In accordance with a normal persistence algorithm. each
`node generates a random number and compares it to the
`value of P. backing oilc and retrying if its random number is
`greater than P. and going forward with the transmission if its
`random number is less than P. ‘The back-01f algorithm uses
`a slot time unique to a wireless network for which the
`invention is designed. using the sum of (a) a “turn-around”
`time corresponding to the time required to switch from
`receiving to transmitting or vice versa. (b) a one-way
`propagation delay time to a most distant node linked to the
`given node. and (c) a carrier detect time.
`For a further understanding of the objects and advantages
`of the invention. reference should be made to the ensuing
`detailed description taken in conjunction with the accom
`panying drawings.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`FIG. 1 is a block diagam of a LAN with a wireless router;
`FIG. 2 is a diagram of a typical network including
`multiple LANs of FIG. 1;
`FIG. 3 is a more detailed drawing of the trunk network
`connection of FIG. 2;
`FIG. 4 is a block diagram of a wireless router system;
`FIG. 5 is a diagram illustrating the counters and data
`structures used by the present invention;
`FIG. 6 is a ?owchart illustrating the determination of
`established links and transmission times utilized by the
`present invention; and
`FIG. 7 is a ?owchart illustrating the comparison to a
`persistence value for transmission according to the present
`invention.
`
`1
`CSMA WITH DYNAMIC PERSISTENCE
`BACKGROUND OF THE lNVENTION
`The present invention relates to determining a persistence
`value P for a P-persistent carrier sense multiple access
`(CSMA) wireless network. in particular a dynamic value of
`persistence (P).
`There are a number of protocols for communication
`between computers at different nodes on a network. In one
`scheme. a centralized station can act as an arbitrator. and
`determine who has access to the network in response to
`requests received from individual network devices (nodes).
`In another scheme. the transmission medium can be divided
`into time slots. with each node being assigned a time slot. In
`yet another system. a token can be passed around the
`network. with a holder of the token having control of the
`network, thus offering a decentralized arbitration scheme.
`Another popular method of network arbitration is a col
`lision detection scheme. Each node accumulates data pack
`ets and waits for the shared channel to clear. In this method.
`each node will transmit when the channel is clear. and
`determine whether its transmission has collided with another
`node. If there is a collision, both nodes will back off for
`di?’erent times and try again. This type of system works well
`for a lightly loaded network, but as the network becomes
`more loaded, more sophisticated modi?cations are needed.
`In one protocol. termed l-persistent CSMA. any node
`transmits immediately if the channel is sensed idle. If the
`channel is sensed busy. each node waits until the channel
`becomes clear. and then transmission is done immediately.
`This type of system works well for a lightly loaded network.
`but can cause collisions in a more heavily loaded network
`due to the “jump on” problem. wherein multiple nodes
`attempt to transmit at the same time.
`Another type of protocol, termed P-persistent CSMA, has
`each node that is ready to transmit generate a random
`number and compare it to a value “P”. Both the random
`number and the value P are between zero and 1. ‘The random
`number is generated so that random numbers will fall
`equally between 0 and 1, so that the probability of the
`random number being less than P is P. and the probability of
`the random number being greater than P is l-P. If the
`random number generated by an individual station is less
`than P. the station transmits immediately. Otherwise, the
`station waits a small amount of time and repeats the proce
`dure. The amount of time delayed is typically a “slot time”.
`which is the amount of time required to determine whether
`another node has tried to transmit. Thus, this amount of time
`includes the propagation delay for a transmission. As can be
`seen. a value of P close to 1 will result in most nodes being
`able to transmit. Thus. for a lightly loaded network. choos
`ing the value of P close to 1 makes sense. For a more heavily
`loaded network. the value of P should be lower. If P is
`chosen as 0.5. for instance. half of the nodes should generate
`a number less than P and half a number greater than P.
`In an article entitled “Link Level Protocols Revisited” by
`Phil Karn and Brian Lloyd, the authors suggested that the
`persistence value for a wireless network should be set
`dynamically. if possible. The authors suggested a back-01f
`algorithm can be viewed as a way to adjust the value of P
`dynamically. since doubling the retransmission interval cor
`responds to halving the value of P. The authors suggested a
`worthwhile research program would be the development of
`good algorithm for the real-time evaluation of P, and sug
`gested that one possible approach would be to use a look-up
`table for determining the value of P based on an estimate of
`the channel activity.
`
`35
`
`45
`
`55
`
`DESCRIPTION OF THE PREFERRED
`EMBODIMENT
`
`65
`
`FIG. 1 illustrates a local area network 10 which has a
`number of individual computers 12 connected by a hard
`wired bus 14 to a wireless router 16. The wireless router is
`connected to an external antenna 18 which may be omnidi
`
`Petitioners' Ex. 1015 - Page 6
`
`

`
`3
`rectional or directional. The wireless router 16 is similar to
`a router used for wired networks. except that it also includes
`a radio for establishing a link with other routers. Other
`computers can also be connected to the LAN. or a single
`computer could be connected to a router 16 in alternate
`embodiments.
`FIG. 2 illustrates a wireless network having multiple
`LANs 10 at different customer sites. As illustrated. these
`IANs can connect via radio transmissions to other LANs 10.
`or to a point of presence (POP) 20. The POPs are access
`points to a wired internetwork. or the ultimate destination of
`tra?ic from the wireless network. The POPs are preferably
`distributed throughout a particular geographic area such that
`a wireless router need only propagate a message through a
`maximum of 3 hops between other wireless routers before
`reaching a POP. The POPs are connected to a backbone
`network 22 which provides a wide area network link.
`As illustrated in more detail in FIG. 3. POP 20 includes
`a number of wireless routers 24 at a single station for
`receiving messages by their corresponding antennas 26. The
`wireless routers 24 are connected via a hard wire line 28 to
`the trunk network 30 which connects to the backbone
`network 22. The trunk network can be either a wire line. a
`microwave transrnis sion medium, a high-speed spread spec
`trum radio. or a satellite link.
`FIG. 4 is a block diagram of a wireless router 16 as shown
`in FIG. 1. As shown. the connection 14 to the LAN bus is
`provided to an input bulfer memory 32 and the CPU 34. The
`CPU provides the data as it is to be transmitted through
`output butter 36 to a radio portion 38 of the router. which
`includes a transmitter 40 and a receiver 42 linked to the
`output buffer by a synchronous BIA-530 link. The transmit
`ter and receiver are connected by an RF cable 44 to antenna
`18.
`CPU 34 controls the operation of the router. and imple
`ments the algorithms of the present invention using data
`stored in a program memory 46. CPU 34 controls the ?ow
`of data to be transmitted. which is ?rst received in bu?’m' 32
`and then transmitted out through butter 36 to the radio 38
`when the appropriate time for transmission is determined. In
`addition. received data provided through bu?’er 36 is routed
`by the CPU 34 to the appropriate computer on LAN 14.
`When CPU 34 receives a packet of data to be transmitted
`in buffer 32. it will ?rst determine the appropriate time for
`transmission. This is done by monitoring the wireless net
`work for transmissions. In a preferred embodiment, the
`transmission is a spread-spectrum transmission. Altemately.
`assigned channels may be used. and the CPU may look at
`one assigned channel. or at several alternatives. If there is a
`transmission occurring on the channel of choice. the CPU
`will wait until an end of the transmission is detected.
`When an end of the transmission is detected. the CPU will
`generate a random number between zero and 1 and compare
`that to its dynamically determined value of P. The value of
`P is determined as a number between 1/(0.5N+1) and
`1/(2N+1). Preferably. Pis set to l/(N+1). N is determined as
`the number of nodes (a) to which there is a link to the given
`node in which CPU 34 is located. and (b) which have
`transmitted within a period of time immediately preceding
`of 5-60 seconds. preferably 10 seconds.
`The value of N is determined using a software routine
`which analyzes data which has been continuously stored and
`updated in memory 46. as illustrated in FIG. 5. As shown. a
`count 48 of the neighbor‘ s to which the given node has a link
`is maintained. Pointers to a location storing information
`about the neighbors are included in the memory at a location
`
`30
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`45
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`55
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`5 1.706.274
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`4
`50. In one example. a location 52 stores an identi?cation of
`a number A. followed by a stored time of last transmission
`54. Neighbor A will be listed if there is a link with that
`neighbor in which the given node can hear the neighbor. and
`the neighbor can hear the given node. The existence of such
`a link is determined by an ADP routine set forth in a
`copending application of the same assignee. entitled
`“ENHANCED ADJACENCY DETECTION PROTOCOL
`FOR WIRELESS APPLICATIONS”. Ser. No. 081526.130.
`?led Sep. 7, 1995. The routine set forth in that application
`determines by a handshaking mechanism whether there is a
`link with any neighbor which the given node hears gener
`ating a transmission and which has not previously been
`determined to be a link neighbor.
`The counter 48 thus indicates the potential maximum
`value of N. with a determination of which of those N nodes
`have transmitted within the last 10 seconds next being
`needed to determine the actual value of N. This is done by
`comparing the current time to the time of last transmission
`in location 54 for each of the neighbor nodes. After that
`determination. the value of N to be used for the persistence
`formula can be generated.
`FIG. 6 illustrates the program for determining a link
`neighbor and time of last transmission. In a ?rst step A. a
`transmission is detected by the given nodes’ radio. Next. it
`is determined whether that neighbor has already been deter
`mined to have a link (step B). If it has. the time of
`transmission is simply updated in the memory in step C.
`Otherwise. a data ?le is opened and the ADP routine is run
`to determine whether there is a link (step D). After the
`determination of a link. the time of transmission is noted
`(Step C)
`FIG. 7 is a ?owchart illustrating the process of determin
`ing when to transmit according to the present invention. In
`a ?rst step E. a data packet for transmission is received by
`the wireless router. The router will determine whether there
`is any transmission on the wireless network. and if there is.
`wait until the transmission ends (step F). Aroutine will then
`be run to determine the value of N (step G). Actually. this
`routine may be constantly run, with N being constantly
`updated so that the new value is available when the trans
`mission actually ends. Once N is determined. the value of
`persistence. P, is determined (step H). A random numbm R
`is then generated (step I) and compared to the value of P
`(step J).
`If R is less than P. the transmission is initiated (step K).
`Otherwise. the router will wait one slot time (step L) and
`then determine if there is any transmission on the wireless
`network (step M). If no tra?ic is detected. the random
`number is generated again (Step I). and. using the same
`value of P and N. and the test for transmission is retried (Step
`J). If there is traffic. the node will wait for the transmission
`to end and then go through the routine again (step F).
`The slot time value used is unique to the present invention
`in the embodiment which uses spread-spectrum radio broad
`casts. The ?rst component of the slot time is the radio
`turnaround time. This is the time for a node which is
`monitoring the network to switch from receiving to trans
`mitting once it has determined that the network is available.
`In one embodiment. this amount of time is approximately
`280 microseconds.
`The next component of the slot time is the one way
`medium propagation delay. This is 5.3 microseconds per
`mile. with 10 miles being assumed to be the worst case for
`the present invention. thus giving 53 microseconds. Since
`this amount of time is much shorter than the other elements
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`Petitioners' Ex. 1015 - Page 7
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`of the slot time, the worst case time is acceptable. However,
`it is possible in other embodiments to optimize the slot time
`on a per node basis to be the propagation delay time to the
`farthest node to which the particular node currently has an
`established link
`The third element of the slot time is the carrier sense time,
`the amount of time required to determine whether there is a
`transmission on the wireless network. This is approximately
`800 microseconds in a preferred embodiment using a spread
`spectrum radio system. This time is affected by the power of
`the operating system in the router. In one embodiment, the
`ADP routine will determine the type of processor (fast or
`slow) used in other nodes. The carrier sense time can then be
`dynamically adjusted to the slowest router a given node is
`linked to. Thus. if all the routers with current links are fast,
`the carrier sense time may be reduced. reducing the overall
`slot time used. This data is stored at position 53 in memory
`46 shown in FIG. 5. This gives a total slot time of 1.133
`milliseconds. As can be seen, the propagation delay time.
`which is typically used as the slot time in a wired network,
`is dwarfed by the other factors. thus requiring a different
`approach in a wireless. radio network. By setting the propa
`gation delay to a worst case. and using other times corre
`sponding to the slowest piece of equipment in the network.
`the slot time should ensure that any other node transmitting
`should be detected, including “hidden” terminals which may
`be in a network range, but may be at a distance beyond the
`current longest link of which the particular node is aware.
`Another factor in the timing is the amount of time
`required to run the software routine to determine the
`dynamic persistence value. Since this requires a fair number
`of calculations. it would not be optimum to constantly run
`this, and thus a minimum period of 5 seconds is used for
`determining relevant transmissions so that constant updating
`is not required. The maximum period of 60 seconds, or the
`optimum period of 10 seconds for considering recent
`transmissions, is used to give an indication of the likelihood
`that the last transmission was close enough that a new
`transmission may occur very shortly.
`The limiting factor of determining whether there is a link
`to a node is also unique to the radio and wireless environ
`ment. If a node is detected by overheating its transmission,
`but that node cannot hear a transmission by the given node,
`then there is no danger of a transmission by the given node
`interfering with the transmission by that overheard node.
`Accordingly, it is not taken into consideration when deter
`mining the value of persistence.
`As will be understood by those familiar with the art, the
`present invention may be embodied in other speci?c forms
`without departing from the spirit or essential characteristics
`thereof. For example, a longer period of time. such as 20
`seconds, or a shorter period, such as 5 seconds can be used
`for including transmitting nodes in the value of N. Different
`slot times could be used. such as any time between 0.8 and
`5 milliseconds. The optimum formula for determining P
`55
`could vary between a denominator of 2N+l and 0.5N+l. The
`method of calculating P or N could be varied, using, for
`instance. hardware circuits rather than a software routine. or
`incrementing counters rather than calculating from the last
`time of transmission. etc. Accordingly, reference should be
`made to the appended claims which set forth the scope of the
`present invention.
`What is claimed is:
`1. A method for dynamically determining the persistence
`value P at a given node in a P-persistent CSMA wireless
`network. comprising the steps of:
`monitoring communications over said wireless network;
`
`50
`
`6
`determining a number N of nodes having transmitted
`within a preceding period of time prior to a request to
`transmit a given message at said given node;
`setting P to a value between 1/(0.5N+l) and 1/(2N+l);
`generating a random number at said given node;
`comparing said random number to P; and
`transmitting said given message from said given node if
`said random number is less than P, otherwise delaying
`at least a delay period of time before transmitting.
`2. The method of claim 1 fm'ther comprising the steps of:
`transmitting to nodes on said wireless network to deter
`mine the existence of a two-way communication link;
`determining a number X of said N nodes in said wireless
`network having a two-way communication link with
`said given node; and
`setting said number N to X for setting said value of P.
`3. The method of claim 1 wherein said preceding period
`of time is between 5 and 60 seconds.
`4. The method of claim 3 wherein said preceding period
`is approximately 10 seconds.
`5. The method of claim 1 wherein said value of P is set to
`1/(N+1).
`6. The method of claim 1 wherein said delay period of
`time is a slot time. said slot time comprising:
`a turn-around time equal to the longer of the time required
`for said node to switch from transmitting to receiving
`and the time required for said node to switch from
`receiving to transmitting. plus
`a one-way propagation delay between said given node and
`a most distant node determined to have a two-way
`communication link with said given node. plus
`a carrier detect time.
`7. The method of claim 6 further comprising the step of
`varying said carrier detect time in accordance with the
`processing speed of said N nodes.
`8. The method of claim 6 fm'ther comprising the step of
`adjusting said one-way propagation delay to a worst case
`value regardless of the distance of actual links.
`9. A method for dynamically determining the persistence
`value P at a given node in a P-persistent CSMA wireless
`network. comprising the steps of:
`monitoring communications over said wireless network;
`transmitting to nodes on said wireless network to deter
`mine the existence of a two-way communication link;
`determining a number X of said nodes in said wireless
`network having a two-way communication link with
`said given node;
`determining a number of N of said X nodes having
`transmitted within a preceding period of time between
`5 and 60 seconds prior to a request to transmit a given
`message at said given node;
`setting P to a value between l/(O.5N+l) and l/(2N+l);
`generating a random number at said given node;
`comparing said random number to P; and
`transmitting said given message from said given node if
`said random number is less than P. otherwise delaying
`at least a delay period of time before transmitting.
`10. The method of claim 9 wherein said value of P is set
`to 1/(N+1).
`11. An apparatus for dynamically determining the persis
`tence value P at a given node in a P-persistent CSMA
`wireless network. comprising:
`means for monitoring communications over said wireless
`network;
`
`30
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`Petitioners' Ex. 1015 - Page 8
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`5,706,274
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`7
`means for determining a number of N of nodes having
`transmitted within a preceding period of time prior to a
`request to transmit a given message at said given node;
`means for setting P to a value between l/(0.5N+1 and
`1/(2N+l);
`means for generating a random number at said given
`node;
`means for comparing said random number to P; and
`means for transmitting said given message from said
`given node if said random number is less than P.
`otherwise delaying at least a delay period of time
`before transmitting.
`12. The apparatus of claim 11 further comprising:
`means for transmitting to nodes on said wireless network
`to determine the existence of a two-way communica
`tion link;
`means for determining a number X of said N nodes in said
`wireless network having a two-way communication
`link with said given node; and
`means for setting said number N to X for setting said
`value of P.
`13. The apparatus of claim 12 wherein said preceding
`period of time is between 5 and 60 seconds.
`14. The apparatus of claim 13 wherein said preceding
`period is approximately 10 seconds.
`15. The apparatus of claim 11 wherein said value of P is
`set to l/(N+l).
`16. The apparatus of claim 11 wherein said delay period
`of time is a slot time, said slot time comprising:
`a turn-around time equal to the longer of the time required
`for said node to switch from transmitting to receiving
`and the time required for said node to switch from
`receiving to transmitting, plus
`
`10
`
`25
`
`8
`a one-way propagation delay between said given node and
`a most distant node determined to have a two-way
`communication link with said given node, plus
`a carrier detect time.
`17. An apparatus for dynamically determining the persis
`tence value P at a given node in a P-persistent CSMA
`wireless network. comprising:
`means for monitoring communications over said wireless
`network;
`means for transmitting to nodes on said wireless network
`to determine the existence of a two-way communica
`tion link;
`means for determining a number X of said nodes in said
`wireless network having a two-way communication
`link with said given node;
`means for determining a number of N of said X nodes
`having transmitted within a preceding period of time
`between 5 and 60 seconds prior to a request to transmit
`a given message at said given node;
`means for setting P to a value between l/(0.5N+1) and
`l/(2N+1);
`means for generating a random number at said given
`node;
`means for comparing said random number to P; and
`means for transmitting said given message from said
`given node if said random number is less than P,
`otherwise delaying at least a delay period of time
`before transmitting.
`18. The apparatus of claim 17 wherein said value of P is
`set to 1/(N+1).
`
`Petitioners' Ex. 1015 - Page 9

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