在API Gateway边缘优化中，可以通过调整各种参数和使用缓存来减少额外的延迟。以下是一些解决方法的代码示例：

1. 合理配置API Gateway的缓存策略，以减少对后端服务的请求：

const express = require('express');
const AWS = require('aws-sdk');
const apigatewaymanagementapi = new AWS.ApiGatewayManagementApi({ apiVersion: '2018-11-29', endpoint: 'YOUR_API_ENDPOINT' });

const app = express();
app.get('/api', (req, res) => {
  // 检查缓存是否存在
  const cacheData = checkCache(req.url);
  if (cacheData) {
    res.send(cacheData);
  } else {
    // 从后端服务获取数据
    const data = fetchDataFromBackendService(req.url);
    // 将数据添加到缓存中
    addToCache(req.url, data);
    res.send(data);
  }
});

function checkCache(url) {
  // 检查缓存是否存在
  // 如果存在，返回缓存数据
  // 否则返回null
}

function addToCache(url, data) {
  // 将数据添加到缓存中
}

function fetchDataFromBackendService(url) {
  // 从后端服务获取数据
  // 并返回数据
}

app.listen(3000, () => {
  console.log('API Gateway caching example app listening on port 3000');
});

2. 使用AWS Lambda来处理API Gateway的请求，以减少额外的网络延迟：

// 使用AWS Lambda处理API Gateway的请求
exports.handler = async (event, context) => {
  // 处理请求
  const response = await processRequest(event);
  return response;
};

async function processRequest(event) {
  // 根据请求参数执行相应的操作
  // 并返回结果
}

3. 启用API Gateway的缓存功能，以减少对后端服务的请求：

Resources:
  ApiGatewayRestApi:
    Type: AWS::ApiGateway::RestApi
    Properties:
      Name: MyApiGateway

  ApiGatewayResource:
    Type: AWS::ApiGateway::Resource
    Properties:
      RestApiId: !Ref ApiGatewayRestApi
      ParentId: !GetAtt ApiGatewayRestApi.RootResourceId
      PathPart: mypath

  ApiGatewayMethod:
    Type: AWS::ApiGateway::Method
    Properties:
      RestApiId: !Ref ApiGatewayRestApi
      ResourceId: !Ref ApiGatewayResource
      HttpMethod: GET
      AuthorizationType: NONE
      Integration:
        Type: AWS_PROXY
        IntegrationHttpMethod: GET
        Uri: arn:aws:apigateway:us-east-1:lambda:path/2015-03-31/functions/arn:aws:lambda:us-east-1:123456789012:function:MyLambda/invocations
        CacheKeyParameters:
          - 'method.request.path.paramname'
        CacheNamespace: mynamespace
        CacheTtlInSeconds: 3600

  ApiGatewayDeployment:
    Type: AWS::ApiGateway::Deployment
    DependsOn: ApiGatewayMethod
    Properties:
      RestApiId: !Ref ApiGatewayRestApi
      Description: API Gateway Deployment

  ApiGatewayStage:
    Type: AWS::ApiGateway::Stage
    Properties:
      RestApiId: !Ref ApiGatewayRestApi
      DeploymentId: !Ref ApiGatewayDeployment
      StageName: Prod

这些代码示例展示了如何通过缓存、使用AWS Lambda来处理请求和启用API Gateway的缓存功能来减少API Gateway边缘优化的额外延迟。请根据实际情况进行相应的调整和配置。