以下是一个示例解决方案，展示了如何使用ASP.NET Core 2.2 Web API创建一个队列后台任务：

1. 创建一个新的ASP.NET Core Web API项目。
2. 添加所需的NuGet包：Microsoft.Extensions.Hosting、Microsoft.Extensions.DependencyInjection、Microsoft.Extensions.Logging和Microsoft.Extensions.Configuration。
3. 在Startup.cs文件中，添加以下代码：

using Microsoft.AspNetCore.Builder;
using Microsoft.AspNetCore.Hosting;
using Microsoft.AspNetCore.Mvc;
using Microsoft.Extensions.Configuration;
using Microsoft.Extensions.DependencyInjection;
using Microsoft.Extensions.Hosting;
using Microsoft.Extensions.Logging;
using System;

namespace WebApiQueueBackgroundTask
{
    public class Startup
    {
        public Startup(IConfiguration configuration)
        {
            Configuration = configuration;
        }

        public IConfiguration Configuration { get; }

        public void ConfigureServices(IServiceCollection services)
        {
            services.AddMvc().SetCompatibilityVersion(CompatibilityVersion.Version_2_2);

            // 注册后台任务服务
            services.AddHostedService();

            // 注册后台任务队列
            services.AddSingleton();

            // 添加日志记录
            services.AddLogging();
        }

        public void Configure(IApplicationBuilder app, IHostingEnvironment env, ILoggerFactory loggerFactory)
        {
            if (env.IsDevelopment())
            {
                app.UseDeveloperExceptionPage();
            }
            else
            {
                app.UseHsts();
            }

            app.UseHttpsRedirection();
            app.UseMvc();
        }
    }
}

4. 创建一个名为QueueBackgroundTask.cs的类文件，实现IQueueBackgroundTask接口，如下所示：

using System;
using System.Threading;
using System.Threading.Tasks;
using Microsoft.Extensions.DependencyInjection;
using Microsoft.Extensions.Hosting;
using Microsoft.Extensions.Logging;

namespace WebApiQueueBackgroundTask
{
    public class QueueBackgroundTask : IQueueBackgroundTask
    {
        private readonly ILogger _logger;
        private readonly IServiceProvider _serviceProvider;

        public QueueBackgroundTask(ILogger logger, IServiceProvider serviceProvider)
        {
            _logger = logger;
            _serviceProvider = serviceProvider;
        }

        public async Task ExecuteAsync(CancellationToken stoppingToken)
        {
            _logger.LogInformation("队列后台任务已启动");

            while (!stoppingToken.IsCancellationRequested)
            {
                using (var scope = _serviceProvider.CreateScope())
                {
                    var scopedProcessingService =
                        scope.ServiceProvider
                            .GetRequiredService();

                    await scopedProcessingService.DoWork(stoppingToken);
                }

                await Task.Delay(TimeSpan.FromSeconds(5), stoppingToken);
            }

            _logger.LogInformation("队列后台任务已停止");
        }
    }
}

5. 创建一个名为ScopedProcessingService.cs的类文件，实现IScopedProcessingService接口，如下所示：

using System;
using System.Threading;
using System.Threading.Tasks;
using Microsoft.Extensions.Logging;

namespace WebApiQueueBackgroundTask
{
    public interface IScopedProcessingService
    {
        Task DoWork(CancellationToken stoppingToken);
    }

    public class ScopedProcessingService : IScopedProcessingService
    {
        private readonly ILogger _logger;

        public ScopedProcessingService(ILogger logger)
        {
            _logger = logger;
        }

        public async Task DoWork(CancellationToken stoppingToken)
        {
            _logger.LogInformation("执行后台任务...");

            // 执行你的后台任务逻辑
            await Task.Delay(TimeSpan.FromSeconds(2), stoppingToken);

            _logger.LogInformation("后台任务执行完成");
        }
    }
}

6. 在QueueBackgroundTaskService.cs文件中，创建一个名为QueueBackgroundTaskService的类，继承自BackgroundService类，如下所示：

using System;
using System.Threading;
using System.Threading.Tasks;
using Microsoft.Extensions.DependencyInjection;
using Microsoft.Extensions.Hosting;
using Microsoft.Extensions.Logging;

namespace WebApiQueueBackgroundTask
{
    public class QueueBackgroundTaskService : BackgroundService
    {
        private readonly ILogger _logger;
        private readonly IServiceProvider _serviceProvider;

        public QueueBackgroundTaskService(ILogger logger, IServiceProvider serviceProvider)
        {
            _logger = logger;
            _serviceProvider = serviceProvider;
        }

        protected override async Task ExecuteAsync(CancellationToken stoppingToken)
        {
            _logger.LogInformation("队列后台任务服务已启动");

            await DoWork(stoppingToken);
        }

        private async Task DoWork(CancellationToken stoppingToken)
        {
            _logger.LogInformation("队列后台任务已启动");

            while (!stoppingToken.IsCancellationRequested)
            {
                using (var scope = _serviceProvider.Create