Method and system for estimating performance metrics in a packet-switched communication network

[0001] This application claims the benefit of U.S. Provisional Application No. 60/157,155, filed Sep. 30, 1999, the entire contents of which are incorporated by reference.

[0002] The present invention relates to packet-switched communication networks, and more particularly to a method and system for estimating traffic between sources and destinations in a communications network.

[0003] Many Internet Service Providers (“ISPs”) provide Enhanced Internet Protocol (“EIP”) real time services such as voice-over IP, fax-over IP, unified messaging, and Internet call waiting over the IP network. The EIP real-time services differ from non-real time, best-effort services provided over Transmission Control Protocol (“TCP”); unlike best-effort services, EIP services have end-to-end quality of service (QOS) requirements for packet loss, delay and delay jitter. As a result, providing EIP services requires new processes for network resource planning.

[0004] Current processes are mostly based on a simple calculation of network link usage. However, this method of planning may result in poor quality for EIP services because it fails to address or estimate end-to-end QOS requirements, such packet loss, delay and delay jitter.

[0005] Although these problems have been addressed by prior art methods, many known methods make Poisson arrival and/or exponential packet length assumptions about service traffic characteristics. In most cases, these assumptions are not applicable for EIP service traffic because different types of services have different packet length and inter-arrival distributions. Even for the same service, e.g. Voice over IP (“VoIP”), different voice encoders generate different traffic statistics. When silence compression capability is de-activated in the encoders, the resulting voice traffic consists of packets with constant length and constant inter-arrival time. Once the silence compression capability is activated, packet inter-arrival times vary.

[0006] Given the mix of many types of deterministic and non-deterministic service traffic, approaches using large deviation theory to estimate end-to-end QOS have been suggested. However, large deviation theory-based estimates assume that there are a fixed number of active sources feeding the network. For example, large deviation theory calculations may assume that there are n₁ voice calls, n₂ fax calls, and n₃ e-mail messaging calls, n₁, n₂, and n₃ being fixed numbers, which are active and that generate traffic at any given time. In reality, the number of active sources feeding the network varies over time because calls are constantly connected and disconnected over any given time period, thereby increasing or decreasing, respectively, the total number of active calls. Thus, a direct application of the large deviation theory as taught by the known art is not the most appropriate method for estimating end-to-end QOS.

[0007] There is need for a process that estimates end-to-end packet loss, delay, and delay jitter for EIP network planning using the large deviation theory while taking into account changes in the number of active sources feeding the network.

[0008] Accordingly, the present invention is directed to a method for estimating end-to-end quality of service (QOS), such as packet loss, delay and delay jitter, in an enhanced IP network for use in network planning. The inventive method includes estimating the blocked traffic and carried traffic from each gateway in the network, determining a possible number N of active sources, using a network routing algorithm to estimate the carried traffic for each network link, calculating at least one QOS characteristic for each network link by varying the number N for each calculation, and estimating an end-to-end QOS characteristic by summing the QOS characteristics for the network links. The inventive method therefore enhances network planning by explicitly taking into account variances in the number of sources when estimating end-to-end QOS, thereby more reflecting real-world operation more accurately.

[0010] FIG. 1 illustrates a preferred embodiment of the inventive method. As is known in the art, an Internet Protocol (“IP”) network contains inter-connected routers. To provide real time IP (“EIP”) services, gateways are deployed at the edge of an IP network. A gateway is connected to a public switched telephone network (“PSTN”) through Primary Rate Interface (“PRI”) links on one side and to the IP network on the other side. The gateway translates between the PSTN and IP networks.

[0011] During network planning, offered call rates to each gateway are estimated. Because each gateway has only a limited number of available PRI links, some of the offered calls may be blocked. Moreover, calls of one service type may experience a higher blocking probability than calls of another type. An equation described in Kaufman, “Blocking in a Shared Resource Environment”, IEEE Transactions on Communications, vol. COM-29, No. 10, October 1981, incorporated herein by reference, is used to determine the probability that calls will be blocked or carried by the network at step 100. Kaufman's algorithm is preferred over an Erlang blocking model because Kaufman's algorithm gives blocking probabilities per type, whereas the Erlang model provides only the blocking probability for the aggregate of all calls.

[0012] The method generally involves first computing the QOS for each individual link and then using the individual link information to estimate the end-to-end QOS. More particularly, steps 102 through 106 involve calculating QOS for each individual link, while steps 108 through 112 use the data obtained with respect to the individual links to estimate end-to-end QOS. At step 102, the process uses the routing algorithm of the IP network to estimate, in Erlangs, the load carried by each link. As understood by those skilled in the art, an Erlang is defined as the aggregate of continuous occupation of a channel for one hour, where an intensity of one Erlang means the channel is continuously occupied.

[0013] The packet loss at a router output link is calculated at step 104. In this step, it is assumed that the bandwidth available to EIP services at a router link is C. In this calculation, it is assumed that there are N_i independent sources of type i, where i=1, . . . , K. Two calls are of the same type if they present same traffic statistics, usually if they employ the same type of voice encoder. For example, a VoIP call and a Voice messaging call may be of the same type if they both use the ITU G.729 standard with silence compression. For each source of type i, R_i and {overscore (R_i)} denote the maximum and average traffic rate of the type i source. Further, in the calculations below, N=(N₁, . . . N_k), R_i=(R₁, . . . R_k), {overscore (R_i)}=({overscore (R₁)}, . . . {overscore (R_k)}). The value N can be either assumed or determined to take on different values to take into account the fact that the number of active sources varies over time in a real-world network.

[0014] Also in the calculation of packet loss for a single output link, for a single source of type i, A_i(t) denotes the number of arrivals of a single type i source in period (0,t). Its asymptotic log moment generating function is: $\begin{array}{cc}{\gamma }_i\left(\Theta \right)=\underset{t->\infty }{\lim }\frac{\log E\left[e^{\Theta A}{i}^{\left(t\right)}\right]}{t}& \left(1\right)\end{array}$
The effective bandwidth function of the type i source is: $\begin{array}{cc}{a}_i\left(\Theta \right)=\frac{{\gamma }_i\left(\Theta \right)}{\Theta }& \left(2\right)\end{array}$

[0015] Next, let G={N:[N·R]>C and [N·{overscore (R)}]<C}, where [N·R] denotes a scalar product of N and R. If the scalar product N·R is less than C, there is no queuing, and therefore no packet delay even if all of the sources transmit at peak rate because the queue has not yet been saturated; in this case, packet delay is caused only by transmission delay. If the scalar product is greater than C, however, the queue is saturated and will experience delays due to an overload of the link. Next, the following equation is solved for Θ. δ(N) is defined as the solution for this equation and will be referenced below in equation (4). $\begin{array}{cc}\sum _{i=1}^K{N}_i{a}_i\left(\Theta \right)=CN\in G& \left(3\right)\end{array}$  NεG  (3)
Next, b is defined as the buffer size of the router output buffer assigned to EIP services. According to large deviation theory, which is known in the art:
P(Q>b|N)˜e^−bδ(N) as b→∞  (4)
where P(Q>b|N) is the loss probability conditioned on N.

[0016] The above definitions and calculations will now be used to calculate the packet loss at the router output link, taking into account changes in the number of active sources N over time. More particularly, when a type i call is admitted into the network and starts to generate packets, it becomes a new active source of type i. When the call completes, the number of active sources N is reduced by one; as a result, N varies over time as calls enter and leave the network. During peak times, there are typically a large number of active sources feeding the link. A Poisson distribution can model the number of active sources in the link as follows: $\begin{array}{cc}P\left(N\right)=\prod _{i=1}^K\frac{{\rho }_i^{\mathrm{Ni}}{e}^{-p_i}}{N_i!}& \left(5\right)\end{array}$
where ρ_i is the offered load of type i service in Erlang. Removing the dependence on N, the probability of packet loss at a router output link is as follows:
$\begin{array}{cc}P\left(Q>b\right)=\sum _{N\in G}P\left(N\right)\times e^{-b\delta \left(N\right)}+\sum _{N\in \left\{\left[N+\stackrel{\_}{R}\right]\right\}>C}P\left(N\right)& \left(6\right)\end{array}$
The calculation in equation (6) takes into account the fact that N varies over time by summing, over all possible values of N, the less probabilities P(Q>b|N) weighted by the probability that N occurs. This expression also assumes that the number of active sources will vary slower than the contents in the buffer. As a result, this estimate more closely reflects the way in which active sources feed into the link.

[0017] Next, at step 106, the inventive method calculates the packet delay for an individual router output link. In this calculation, D is a random variable representing the packet delay at a Touter output link. The packet delay distribution may be obtained from packet loss at the router output link, which was calculated in step 104, as follows:
P(D>d)=P(Q/C>d)=P(Q>dC)  (7)
where C is the output link speed.

[0018] At this point, the probability of both packet loss and packet delay at an individual router output link has been calculated for all possible values of N active sources, thereby taking into account changes in the number of active sources in the network. Next, steps 108 through 112 take the single link statistic calculations from steps 102 through 106 and use them to calculate end-to-end packet statistics.

[0019] Step 108 of the inventive method involves calculating the end-to-end packet loss. In this calculation, it is assumed that the losses occur independently along the end-to-end path and that there are a total number of L router output links. Preferably, the loss and delay characteristics for each one of the L router output links is calculated according to steps 104 and 106 described above. With respect to the end-to-end packet loss calculation at step 108, p_i is defined as the loss probability of an ith link along the path. The total end-to-end loss probability along the path is then calculated to be: $\begin{array}{cc}l-\prod _{i=1}^L\left(1-p_i\right)& \left(8\right)\end{array}$

[0020] Next, the end-to-end packet delay is calculated at step 110. In this calculation, it is assumed that the delay for each individual packet occurs independently, without being influenced by delays in other packets along the path. To calculate the end-to-end packet delay, f_i(x) is the delay distribution of the ith link along the path. The end-to-end delay distribution along the path is therefore defined as:
f(x)=f₁(x){circle around (×)}f₂(x) . . . {circle around (×)}f_L(x)  (9)
where f(x) is the end-to-end delay distribution and {circle around (×)} denotes convolution. More specifically, the end-to-end delay distribution is the convolution of the link delay distributions along the path.

[0021] Next, at step 112, the inventive process calculates the end-to-end packet delay jitter. In this step, the user can select a specific delay jitter percentage p for the ten computation (e.g., 95%, 98% or 99% delay jitters). Delay jitter is defined as t₂−t₁, where (100−p)/2 percent of packets experience delays less than t₁ ms and (100−p)/2 percent of packets experience delays greater than t₂ ms. In particular, t₁ and t₂ are found by solving the following equations.
∫₀^t1f(x)dx=p/2 ∫_t2^∞f(x)dx=p/2  (10)

[0022] Thus, the inventive method estimates end-to-end QOS by first estimating the amount of traffic blocked and carried by the network, preferably using Kaufman's algorithm, estimating single link statistics for each individual router output link in a path, taking into account variations in the number of active sources, and then using the single link statistics to calculate end-to-end QOS. In these calculations, it is assumed that the estimates of offered traffic for each service to each gateway is given, preferably in Erlangs. By calculating the loss and delay probability for all possible N number of active sources, as described by way of example in Equations (5) through (10), the inventive method provides abetter estimate of network traffic because it considers the fact that the number of active sources will vary over time.

[0023] The inventive method can be carried out in any known network system. The system can include a database that contains the parameters (e.g. service type and characteristics) for each gateway in the system, a memory that stores an end-to-end quality service program corresponding to the inventive method, and a processor that executes the end-to-end quality service program according to the steps shown in FIG. 1. From the inventive method, the system can output network information such as Wide Area Network (“WAN”) link utilization; one-way packet loss; one-way and two-way packet delay and delay jitter; gateway Primary Rate Interface (“PRI”) link utilization and blocking probabilities per physical location; and/or global maximum PRI link utilization and maximum blocking probability.

[0024] An Internet Service Provider (“ISP”) can therefore estimate network performance using the inventive method and system and, if QOS requirements are not met, reallocate sources and conduct the inventive method again quickly and easily to assess the effect of the reallocation on network performance. For example, the ISP may experiment with different traffic scenarios to distribute global origination traffic among network cities in different ways.

[0025] It should be understood that various alternatives to the embodiments of the invention described herein may be employed in practicing the invention. It is intended that the following claims define the scope of the invention and that the method and apparatus within the scope of these claims and their equivalents be covered thereby.