TSIN01 Information Networks Lecture 3

Transcription

1 TSIN01 Information Networks Lecture 3 Danyo Danev Division of Communication Systems Department of Electrical Engineering Linköping University, Sweden September 10 th, 2018 Danyo Danev TSIN01 Information Networks Lecture 3 1 / 24

2 Lecture overview Agenda Multiaccess communication Multiaccess media Idealized slotted multiaccess model Danyo Danev TSIN01 Information Networks Lecture 3 2 / 24

3 Multiaccess communication media Point-to-point communication links: twisted pairs of wires, coaxial cables, optical fibers, microwave radio links The received signal on each link depends only on the transmitted signal, the properties of the link and noise strength Multiaccess communication media: satellite systems, radio broadcast, multidrop telephone lines, multitap bus systems The received signal on one node depends on the transmitted signals from a set of other nodes, the properties of the link and noise strength Multiaccess media form the basis for LANs, MANs, satellite networks, and radio networks Danyo Danev TSIN01 Information Networks Lecture 3 3 / 24

4 Satellite channels In geosynchronous communication satellite systems, many ground stations transmit to a common satellite receiver The received messages are relayed to the ground stations Danyo Danev TSIN01 Information Networks Lecture 3 4 / 24

5 Satellite channels If several stations transmit at the same time and frequency band, their signals are garbled and incorrectly received Satellites often have separate antenna beams for different geographical areas, allowing independent reception and relaying between areas FDM or TDM can be used to make the satellite channel a collection of virtual point-to-point links Problem is same (increased delay and underutilization) with serving multiple sessions on one point-to-point link Sharing the medium on a demand basis reduces the delay and increases utilization Demand sharing is more difficult than in point-to-point links, cause earth stations are not aware of the instantaneous traffic of other earth stations Danyo Danev TSIN01 Information Networks Lecture 3 5 / 24

6 Multidrop telephone lines Connect one primary node with many secondary nodes Signal of primary node is received by all secondary ones Sum of secondary nodes received by primary node Major problem is sharing the channel secondary to primary Polling avoids interference, but is inefficient Danyo Danev TSIN01 Information Networks Lecture 3 6 / 24

7 Multitapped bus Each node can receive the signal sent by each other node If many nodes transmit at the same time, the received signal is garbled Nodes directly overhearing each other has important practical consequences in the design of access protocols Danyo Danev TSIN01 Information Networks Lecture 3 7 / 24

8 Packet radio networks Each node can receive from a subset of (not all) other nodes This makes packet radio networks far more complex If many nodes in the subset transmit at the same time, the received signal is garbled Danyo Danev TSIN01 Information Networks Lecture 3 8 / 24

9 MAC sublayer The multiaccess medium is allocated to the nodes by the Medium Access Control (MAC) sublayer, which lies between the PHY and DLC layers Implication: the separation of functions between layers is not as clear as in point-to-point links Feedback on transmission errors is part of LLC in DLC, but also required for allocation (thus flow control) in MAC Routing is automatically implemented due to the broadcast nature of multiaccess channels Danyo Danev TSIN01 Information Networks Lecture 3 9 / 24

10 Queueing view Multiaccess communication in queueing terms: each node has a queue of packets to be transmitted; the multiaccess channel is a common server Ideally, the server views all the waiting packets as one combined queue to be served by a queueing discipline But, the server doesn t know which nodes contain packets Also, the nodes are unaware of packets at other nodes Interesting part of multiple access problem is that the knowledge about the state of the queue is distributed Danyo Danev TSIN01 Information Networks Lecture 3 10 / 24

11 Extreme strategies Two extreme strategies for the multiaccess problem: 1. Free-for-all approach: nodes send new packets immediately, hoping for no interference from other nodes When and how packets are retransmitted when collisions (interference) occur? 2. Perfectly scheduled approach: there is some order (e.g. round robin) in which nodes receive reserved intervals for channel use What determines the scheduling order? (it can be dynamic) How long can a reserved interval last? How are nodes informed about their turn? Danyo Danev TSIN01 Information Networks Lecture 3 11 / 24

12 Recap - Multiaccess problem A set of nodes share a multiaccess communication channel If two or more nodes transmit simultaneously, reception is garbled If none transmit, the channel is unused Problem statement: coordinate the use of channel so that exactly one node is transmitting at every instance of time We use a highly idealized model that allows us to focus on the contention problem occurring when multiple nodes attempt to use the channel simultaneously Danyo Danev TSIN01 Information Networks Lecture 3 12 / 24

13 Idealized slotted multiaccess model System: m transmitting nodes and 1 receiver node Assumption 1: Slotted system All packets have same length Each packet needs one time unit (a slot) for transmission All transmitters are synchronized so that reception starts at an integer time and ends before next integer time Comments: With slots the system is discrete-time and easier analyzed Carrier sensing and early collision detection are precluded (for the moment; later, the model will be extended) Synchronization of transmitters is not entirely trivial; it requires stable clocks, feedback and guard time Danyo Danev TSIN01 Information Networks Lecture 3 13 / 24

14 Idealized slotted multiaccess model Assumption 2: Poisson arrivals Packets arrive at each of the m transmitting nodes according to independent identical Poisson processes Let λ be the overall packet arrival rate to the system Let λ/m be the packet arrival rate at each node Comments: Poisson arrivals are unrealistic for multipacket messages, since the packet arrivals are correlated Danyo Danev TSIN01 Information Networks Lecture 3 14 / 24

15 Poisson process The arrival instants are derived from a Poisson process X(t) with intensity parameter λ (packets/sec) The number of packets k that arrive during an interval [t 0, t 0 + t] of duration t is Poisson distributed: P r{x(t) = k} = (λt)k e λt k! On average, λt packets arrive in an interval of duration t The difference between the arrival times of two consecutive messages is exponentially distributed with average 1/λ P r{t i+1 t i = τ} = f(τ) = λe λτ Danyo Danev TSIN01 Information Networks Lecture 3 15 / 24

16 Idealized slotted multiaccess model Assumption 3: Collision or perfect reception If two or more nodes send in a given time slot, there is a collision and the receiver obtains no information about the content or sources of the transmitted packets If just one node sends, the packet is correctly received Comments: Perfect reception ignores the possibility of errors due to noise, channel impairments, etc Collision ignores the possibility that a receiver can successfully decode one transmission in the presence of other transmissions Danyo Danev TSIN01 Information Networks Lecture 3 16 / 24

17 Idealized slotted multiaccess model Assumption 4: (0, 1, e) Immediate Feedback At the end of each slot, each node obtains feedback specifying how any packets were transmitted in that slot 0 zero packets (idle) 1 one packet(successful transmission) e more that one packet (collision/error) Comments: Immediate feedback is unrealistic for channels with large propagation delay, such as the satellite channels This assumption simplifies the analysis; delayed or limited feedback complicates the analysis Danyo Danev TSIN01 Information Networks Lecture 3 17 / 24

18 Idealized slotted multiaccess model Assumption 5: Retransmission of collisions Each packet involved in a collision will be retransmitted in some later slot, until it is successfully received A node with a packet that must be retransmitted is said to be backlogged Comments: This assumption is reasonable in providing reliable communication Practical retransmission protocols (e.g. ARQ - Automatic Repeat request) allow a limited number of retransmissions Danyo Danev TSIN01 Information Networks Lecture 3 18 / 24

19 Idealized slotted multiaccess model Regarding buffering capabilities, one of the two following assumptions is made: Assumption 6a: No-buffering If one packet at a node is currently waiting for transmission or colliding with another packet during transmission, new arrivals at that node are discarded and never transmitted Assumption 6b: Infinite set of nodes (m = ) The system has an infinite set of nodes and each newly arriving packet arrives at a new node Danyo Danev TSIN01 Information Networks Lecture 3 19 / 24

20 Discussion of no-buffering assumption 6a Appears peculiar, since new arrivals in backlogged nodes are discarded, whereas packets once transmitted must be retransmitted until they are successfully received Interest is on channels with large number of nodes, relatively small arrival rate λ, and small required delay (conditions where TDM is inefficient) Then, the fraction of backlogged nodes is small and new arrivals at them are almost negligible Thus, the delay is relatively close to one with buffering Gives a lower bound to the delay of practical systems In practice, there is some buffering and some form of flow control to avoid buffer overflow Danyo Danev TSIN01 Information Networks Lecture 3 20 / 24

21 Discussion of infinite-node assumption 6b Provides an upper bound for the delay achieved with a finite number of nodes Each node (of a finite set) can consider itself as a set of virtual nodes, one for each arriving packet Virtual nodes apply any given multiaccess algorithm independently, equivalently to having infinite nodes A node with several backlogged packets will sometimes send them in one slot causing a sure collision In practice, the delay is smaller, since sure collisions are avoided and there is a finite number of nodes and buffering If bounds are close, approximation is good Assumption 6b is more accurate, but 6a is less abstract Danyo Danev TSIN01 Information Networks Lecture 3 21 / 24

22 Throughput Individual throughput is the expected number of packets that are delivered to the receiver in a unit time The system throughput is the sum of the individual throughputs For a stable system with infinite buffering the throughput is equal to the message arrival rate It is measured in packets/sec, symbols/sec, bits/sec Danyo Danev TSIN01 Information Networks Lecture 3 22 / 24

23 Delay The time difference between the arrival of a packet to the receiver node and the sender node If the information flow is modeled by a stochastic process, the delay is a positive real-valued stochastic variable The distribution function and the mean value of the delay are of interest The delay indicates whether the system is stable or not In an ideal system we assume unlimited buffer storage Danyo Danev TSIN01 Information Networks Lecture 3 23 / 24

24 Next lecture Agenda Slotted ALOHA, definition Slotted ALOHA, instructive analysis Slotted ALOHA, rigorous analysis Little s theorem Danyo Danev TSIN01 Information Networks Lecture 3 24 / 24