Section 1.4: Delay, loss, and throughput in packet switched networks

average throughput

f the file consists of F bits and the transfer takes T seconds for Host B to receive all F bits, then the average throughput of the file transfer is F/T bits/sec.

Traceroute

When the user specifies a destination hostname, the program in the source host sends multiple, special packets toward that destination. As these packets work their way toward the destination, they pass through a series of routers. When a router receives one of these special packets, it sends back to the source a short mes- sage that contains the name and address of the router.

If La/R > 1

average rate at which bits arrive at the queue exceeds the rate at which the bits can be transmitted from the queue. In this unfortunate situation, the queue will tend to increase without bound and the queuing delay will approach infinity! Therefore, one of the golden rules in traffic engineering is: Design your system so that the traffic intensity is no greater than 1.

transmission delay

Denote the length of the packet by L bits, and denote the transmission rate of the link from router A to router B by R bits/sec. For example, for a 10 Mbps Ethernet link, the rate is R = 10 Mbps; for a 100 Mbps Ethernet link, the rate is R = 100 Mbps. The transmission delay is L/R. This is the amount of time required to push (that is, transmit) all of the packet's bits into the link.

calculating propagation delay

The propagation delay is the distance between two routers divided by the propagation speed. That is, the propagation delay is d/s, where d is the distance between router A and router B and s is the propagation speed of the link.

processing delay

The time required to examine the packet's header and determine where to direct the packet is part of the processing delay. The processing delay can also include other factors, such as the time needed to check for bit-level errors in the packet that occurred in transmitting the packet's bits

propagation delay.

The time required to propagate from the beginning of the link to router B is the propagation delay. The bit propagates at the propagation speed of the link. The propagation speed depends on the physical medium of the link (that is, fiber optics, twisted-pair copper wire, and so on) and is in the range of 2 108 meters/sec to 3 108 meters/sec which is equal to, or a little less than, the speed of light.

how is the actual arrival process to a queue

Typ- ically, the arrival process to a queue is random; that is, the arrivals do not follow any pattern and the packets are spaced apart by random amounts of time. In this more realistic case, the quantity La/R is not usually sufficient to fully characterize the queueing delay statistics. Nonetheless, it is useful in gaining an intuitive understand- ing of the extent of the queuing delay. In particular, if the traffic intensity is close to zero, then packet arrivals are few and far between and it is unlikely that an arriving packet will find another packet in the queue. Hence, the average queuing delay will be close to zero. On the other hand, when the traffic intensity is close to 1, there will be intervals of time when the arrival rate exceeds the transmission capacity (due to variations in packet arrival rate), and a queue will form during these periods of time; when the arrival rate is less than the transmission capacity, the length of the queue will shrink. Nonetheless, as the traffic intensity approaches 1, the average queue length gets larger and larger.

queuing delay

At the queue, the packet experiences a queuing delay as it waits to be transmitted onto the link. The length of the queuing delay of a specific packet will depend on the num- ber of earlier-arriving packets that are queued and waiting for transmission onto the link.

why can't packet delays approach infinity?

In reality a queue preceding a link has finite capacity, although the queuing capacity greatly depends on the router design and cost. Because the queue capacity is finite, packet delays do not really approach infinity as the traffic intensity approaches 1.

propagation delay time

In wide-area networks, propagation delays are on the order of milliseconds.

traffic intensity

La/R plays an important role in estimating the extent of the queuing delay. let a denote the average rate at which packets arrive at the queue (a is in units of packets/sec). Recall that R is the transmission rate; that is, it is the rate (in bits/sec) at which bits are pushed out of the queue. Also suppose, for simplicity, that all packets consist of L bits.

transmission rate of the bottleneck link

Let Rs denote the rate of the link between the server and the router; and Rc denote the rate of the link between the router and the client. Suppose that the only bits being sent in the entire network are those from the server to the client. We now ask, in this ideal scenario, what is the server- to-client throughput? the throughput is min{Rc, Rs}, that is, it is the transmission rate of the bottleneck link.

queuing delay time

Queuing delays can be on the order of microseconds to milliseconds in practice.

Comparing Transmission and Propagation Delay

The transmission delay is the amount of time required for the router to push out the packet; it is a function of the packet's length and the trans- mission rate of the link, but has nothing to do with the distance between the two routers. The propagation delay, on the other hand, is the time it takes a bit to propagate from one router to the next; it is a function of the distance between the two routers, but has nothing to do with the packet's length or the transmission rate of the link.

transmission delay time

Transmission delays are typically on the order of microseconds to milliseconds in practice.

what happens when there is no place to store an arriving packet in the queue?

a packet can arrive to find a full queue. With no place to store such a packet, a router will drop that packet; that is, the packet will be lost.

what happens during a packet loss?

a packet loss will look like a packet having been transmitted into the network core but never emerging from the network at the destination. The fraction of lost packets increases as the traffic intensity increases. Therefore, performance at a node is often measured not only in terms of delay, but also in terms of the probability of packet loss.

instantaneous throughput

at any instant of time is the rate (in bits/sec) at which Host B is receiving the file. (Many applications, including many P2P file sharing systems, display the instantaneous throughput during downloads in the user interface—perhaps you have observed this before!) it is desirable to have the highest possible throughput.

suppose there are N-1 routers between the source host and the destination host. Let's also suppose for the moment that the network is uncon- gested (so that queuing delays are negligible), the processing delay at each router and at the source host is dproc, the transmission rate out of each router and out of the source host is R bits/sec, and the propagation on each link is dprop. The nodal delays accumulate and give an end-to-end delay,

dend-end = N (dproc + dtrans + dprop)

significance of each of the delays

dprop can be negligible (for example, a couple of microseconds) for a link connect- ing two routers on the same university campus; however, dprop is hundreds of mil- liseconds for two routers interconnected by a geostationary satellite link, and can be the dominant term in dnodal. Similarly, dtrans can range from negligible to significant. Its contribution is typically negligible for transmission rates of 10 Mbps and higher (for example, for LANs); however, it can be hundreds of milliseconds for large Internet packets sent over low-speed dial-up modem links. The processing delay, dproc, is often negligible; however, it strongly influences a router's maximum throughput, which is the maximum rate at which a router can forward packets.

packet suffers from several types of delays at each node along the path. The most important of these delays are

nodal processing delay, queuing delay, transmis- sion delay, and propagation delay; together, these delays accumulate to give a total nodal delay.

processing delay time

in high speed routers it is typically microseconds or less.

throughput

the amount of data per second that can be trans- ferred

as the traffic intensity approaches 1

the average queuing delay increases rapidly. A small percentage increase in the intensity will result in a much larger percentage-wise increase in delay.

nodal delay

the delay at a single router.

how does trace route work?

there are N 1 routers between the source and the destination. Then the source will send N special packets into the network, with each packet addressed to the ultimate destination. These N special packets are marked 1 through N, with the first packet marked 1 and the last packet marked N. When the nth router receives the nth packet marked n, the router does not forward the packet toward its destination, but instead sends a message back to the source. When the des- tination host receives the Nth packet, it too returns a message back to the source. The source records the time that elapses between when it sends a packet and when it receives the corresponding return message; it also records the name and address of the router (or the destination host) that returns the message.

A packet can be transmitted on a link only if

there is no other packet currently being transmitted on the link and if there are no other packets preceding it in the queue

transmission rate of a packet

transmission rates of the N links being R1, R2,..., RN. Applying the same analysis as for the two-link network, we find that the throughput for a file transfer from server to client is min{R1, R2,..., RN}, which is once again the trans-