Exemplo de Uso de Modelos Analíticos
Redes de Filas

Francisco Heron de Carvalho Junior

Analysis of Open Queueing Networks

Definitions (Box 34.1)

Inputs

X = external arival rate, system throughput
= service time per visit to the ith device
= number of visits to the ith device
M = number of devices (not including terminals)

Outputs

= mean number of jobs at ith device
R = response time of the ith device
R = system response time
= utilization of the ith device
= mean number of jobs in the system

Example

Figure 1 shown below represents a queueing model of a server consisting of a CPU and two disks, A and B. Measurements on a distributed system with six clients making requests to the file server produced the following data:

Based on these observations, we can compute the service demands and visit ratios as follows:

We now have all the input parameters required to analyse the system.

The model can be used to answer some of the typical questions. For example, we might want to quantify the impact of the following changes:
1. Increase the number of clients to B
2. Use a cache for disk B with a hit rate of 50%, although it increases the CPU overhead by 30% and the disk B service time (per I/O) by 10%.
3. Have a lower cost server with only one disk (disk A) and direct all I/O requests to it.

1st Case:

The first question can be answered if we assume that the new clients make requests similar to those measured. The request arrival rate will go up by a factor of . Since the arrival rate was three requests per second, with more clients it will become four requests per second. The new analysis is as follows:

Thus, if the number of clients is increased from 6 to 8, the server response time will degrade by a factor of

2nd case:

The second question requires changing , and as follows:

The analysis of the changed systems is as follows

Thus, if we use a cache for disk B, the server response time will improve by a factor of

3rd case

The third question requires adjusting and . We assume that there is enough space on disk A to be able to accomodate all files on both disks The analysis is as follows:

Sensibility Analisys over the parameters (service time per visit to the ith device)

For Disk A

For Disk B

For CPU

Sensibility Analisys over the parameter X (system throghput)