ServiceStack doesn't have a configurable concurrency model per AppHost, it is dependent upon the AppHost that your ServiceStack services are hosted with:
ASP.NET Host (AppHostBase)
For ASP.NET web hosts, ServiceStack doesn't create any new threads itself, the requests are simply handled on the same IIS/Nginx/etc ASP.NET HTTP WebWorker that handles the request.
HttpListener Self-Host (AppSelfHostBase)
The default Self-Host HttpListener option for ServiceStack that executes requests on the SmartThreadPool managed ThreadPool. By default it executes on Environment.ProcessorCount * 2 or maximum of 16 worker threads. See this chart for the performance of the different ServiceStack Hosts.
HttpListener Pool Self-Host (AppHostHttpListenerPoolBase)
This is another Self-Host HttpListener option for ServiceStack that uses its own managed ThreadPool to execute requests on (free-ing up the HttpListener async callback thread). The default poolSize of the ThreadPool is 500 threads, though this is configurable in the AppHostHttpListenerPoolBase(serviceName, handlerPath, poolSize, assembliesWithServices) constructor.
HttpListener Single Self-Host (AppHostHttpListenerBase)
ServiceStack only creates a new thread on Startup when you call new AppHost().Start(url). There are no new threads created at run-time, i.e. the request is handled on the HttpListener async callback thread.
RedisMQ Host (RedisMqServer)
A good option for managing long-running tasks is to delegate requests to a Redis MQ Host which is a light-weight MQ Server allowing you to defer and process requests in managed background threads. By default the RedisMqServer spawns a single background thread for each Message type (i.e. Request), though this is configurable on start-up, e.g: in the example below 2 background threads are used to handle PostTwitter requests, whilst only 1 background thread each is used to process CallFacebook and EmailMessage requests:
mqServer.RegisterHandler<PostTwitter>(ServiceController.ExecuteMessage, noOfThreads:2);
mqServer.RegisterHandler<CallFacebook>(ServiceController.ExecuteMessage);
mqServer.RegisterHandler<EmailMessage>(ServiceController.ExecuteMessage);