Added Erlang distribution

README.md

@@ -205,11 +205,11 @@ minutes, in this case:
 ## Using other distributions
 
 Although the Markov process is the most commonly used to model queueing systems,
-your particular use case may be better modeled by some process. For example, in
-many applications, batch jobs are triggered periodically by some scheduler
-like [cron]. The service time may still be exponentially distributed, but the
-inter-arrival time is now deterministic. To model these situations, use the
-lower-level API provided by the _general_ process:
+your particular use case may be better modeled by some other process. For
+example, in many applications, batch jobs are triggered periodically by some
+scheduler like [cron]. The service time may still be exponentially distributed,
+but the inter-arrival time is now deterministic. To model these situations, use
+the lower-level API provided by the `general` process:
 
 ```ts
 const simulator = BatchSimulator.general(stack);
@@ -225,9 +225,10 @@ const report = simulator.simulate([{
 }]);
 ```
 
-If you need to use some more probability distribution that is not available in
-the `Distribution` class, you can bring your own, by implementing the
-`IDistribution` interface.
+In addition to deterministic and exponential distributions, the simulator also
+offers an implementation of the [Erlang distribution]. But If you need to use
+some probability distribution that is not available in the `Distribution` class,
+you can bring your own, by implementing the `IDistribution` interface.
 
 ## Unsupported features (yet)
 
@@ -248,4 +249,6 @@ Some of the AWS Batch features are not being simulated by this library:
 
 [mmc]: https://www.wikiwand.com/en/M/M/c_queue
 
-[cron]: https://en.wikipedia.org/wiki/Cron
+[cron]: https://en.wikipedia.org/wiki/Cron
+
+[Erlang distribution]: https://en.wikipedia.org/wiki/Erlang_distribution

src/random.ts

@@ -26,6 +26,10 @@ export interface IDistribution {
 
 export class Distribution {
   static deterministic(value: number): IDistribution {
+    if (value <= 0) {
+      throw new Error(`The deterministic time must be positive. Got ${value}`);
+    }
+
     return new class implements IDistribution {
       nextTime(): number {
         return value;
@@ -34,9 +38,29 @@ export class Distribution {
   }
 
   static exponential(lambda: number): IDistribution {
+    if (lambda <= 0) {
+      throw new Error(`The parameter of the exponential distribution must be positive. Got ${lambda}`);
+    }
+
+    return this.erlang(1, lambda);
+  }
+
+  static erlang(k: number, lambda: number): IDistribution {
+    if (lambda <= 0) {
+      throw new Error(`The rate parameter (λ) of the Erlang distribution must be positive. Got ${lambda}`);
+    }
+
+    if (!(Number.isInteger(k) && k > 0)) {
+      throw new Error(`The shape parameter (k) of the Erlang distribution must be a positive integer. Got ${k}`);
+    }
+
     return new class implements IDistribution {
       nextTime(): number {
-        return -Math.log(Math.random()) / lambda;
+        let sum = 0;
+        for (let i = 0; i < k; i++) {
+          sum += Math.log(Math.random());
+        }
+        return -sum / lambda;
       }
     };
   }