[apm serverless] Add examples using trace_continuation_strategy to sampling docs (#4210)

* port #4167 to serverless

* Update docs/en/serverless/apm/apm-transaction-sampling.mdx

Co-authored-by: DeDe Morton <[email protected]>

---------

Co-authored-by: DeDe Morton <[email protected]>

Author: colleenmcginnis

docs/en/serverless/apm/apm-transaction-sampling.mdx

@@ -28,23 +28,69 @@ Head-based sampling is quick and easy to set up.
 Its downside is that it's entirely random — interesting
 data might be discarded purely due to chance.
 
-### Distributed tracing with head-based sampling
+### Distributed tracing
 
 In a _distributed_ trace, the sampling decision is still made when the trace is initiated.
 Each subsequent service respects the initial service's sampling decision, regardless of its configured sample rate;
 the result is a sampling percentage that matches the initiating service.
 
-In this example, `Service A` initiates four transactions and has sample rate of `.5` (`50%`).
-The sample rates of `Service B` and `Service C` are ignored.
+In the example in _Figure 1_, `Service A` initiates four transactions and has a sample rate of `.5` (`50%`).
+The upstream sampling decision is respected, so even if the sample rate is defined and is a different
+value in `Service B` and `Service C`, the sample rate will be `.5` (`50%`) for all services.
+
+**Figure 1. Upstream sampling decision is respected**
 
 ![Distributed tracing and head based sampling example one](../images/apm-dt-sampling-example-1.png)
 
-In this example, `Service A` initiates four transactions and has a sample rate of `1` (`100%`).
-Again, the sample rates of `Service B` and `Service C` are ignored.
+In the example in _Figure 2_, `Service A` initiates four transactions and has a sample rate of `1` (`100%`).
+Again, the upstream sampling decision is respected, so the sample rate for all services will
+be `1` (`100%`).
+
+**Figure 2. Upstream sampling decision is respected**
 
 ![Distributed tracing and head based sampling example two](../images/apm-dt-sampling-example-2.png)
 
-### OpenTelemetry with head-based sampling
+### Trace continuation strategies with distributed tracing
+
+In addition to setting the sample rate, you can also specify which _trace continuation strategy_ to use.
+There are three trace continuation strategies: `continue`, `restart`, and `restart_external`.
+
+The **`continue`** trace continuation strategy is the default and will behave similar to the examples in
+the [Distributed tracing section](#distributed-tracing).
+
+Use the **`restart_external`** trace continuation strategy on an Elastic-monitored service to start
+a new trace if the previous service did not have a `traceparent` header with `es` vendor data.
+This can be helpful if a transaction includes an Elastic-monitored service that is receiving requests
+from an unmonitored service.
+
+In the example in _Figure 3_, `Service A` is an Elastic-monitored service that initiates four transactions
+with a sample rate of `.25` (`25%`). Because `Service B` is unmonitored, the traces started in
+`Service A` will end there. `Service C` is an Elastic-monitored service that initiates four transactions
+that start new traces with a new sample rate of `.5` (`50%`). Because `Service D` is also
+Elastic-monitored service, the upstream sampling decision defined in `Service C` is respected.
+The end result will be three sampled traces.
+
+**Figure 3. Using the `restart_external` trace continuation strategy**
+
+![Distributed tracing and head based sampling with restart_external continuation strategy](../images/apm-dt-sampling-continuation-strategy-restart_external.png)
+
+Use the **`restart`** trace continuation strategy on an Elastic-monitored service to start
+a new trace regardless of whether the previous service had a `traceparent` header.
+This can be helpful if an Elastic-monitored service is publicly exposed, and you do not
+want tracing data to possibly be spoofed by user requests.
+
+In the example in _Figure 4_, `Service A` and `Service B` are Elastic-monitored services that use the
+default trace continuation strategy. `Service A` has a sample rate of `.25` (`25%`), and that
+sampling decision is respected in `Service B`. `Service C` is an Elastic-monitored service that
+uses the `restart` trace continuation strategy and has a sample rate of `1` (`100%`).
+Because it uses `restart`, the upstream sample rate is _not_ respected in `Service C` and all four
+traces will be sampled as new traces in `Service C`. The end result will be five sampled traces.
+
+**Figure 4. Using the `restart` trace continuation strategy**
+
+![Distributed tracing and head based sampling with restart continuation strategy](../images/apm-dt-sampling-continuation-strategy-restart.png)
+
+### OpenTelemetry
 
 Head-based sampling is implemented directly in the APM agents and SDKs.
 The sample rate must be propagated between services and the managed intake service in order to produce accurate metrics.