Discrete-Event Simulation

abu@software-lab.de

# Discrete-Event Simulation (DES)

(c) Software Lab. Alexander Burger

PicoLisp has a Discrete-Event Simulation library in `"@lib/simul.l"`.

- Implementation
- Global Variables
- Functions
- Usage
- An Example

## Implementation

The simulated objects (often called "Agents") are implemented as separate coroutines. These are created the normal way with co, and the library functions use yield to transfer control between them.

Only one coroutine may be running at one point in time. All others are either

- ready to run,
- waiting for the next scheduled point in time, and/or
- waiting for one or several specific signals (events).

A running coroutine can suspend itself, and cause another coroutine to resume, by either

- passing control to the next coroutine, or
- pausing for a given amount of time and/or waiting for signals.

The simulation can optionally run in realtime mode. In that case, it sleeps between the scheduled points in time, and accepts key strokes for user interaction.

The library consists of five global variables and four functions.

## Global Variables

`*Time`
  Simulated system time since the start of the simulation. It can be in any unit, but should be in milliseconds if in realtime mode.
`*Ready`
  Queue of coroutines ready to run.
`*Next`
  idx tree of coroutines pausing for a given time.
`*Rt`
  Realtime: Either `NIL` (default), or 1 for wall clock speed, 2 for double speed etc.
`*Keys`
  Holds possibly queued key presses (only in realtime mode).

## Functions

`(des [. prg])`
  Performs one discrete-event simulation step. It first runs all coroutines in `*Ready` until that queue is empty. Then - if `*Next` is not empty - advances the simulation to the next point in time, and resumes all corresponding coroutines. In that case, if in realtime mode, it delays execution as necessary, handles possible key presses, and runs `prg` after each key.
`(pause ['cnt|sym] ..) -> any`
  Waits for events (i.e. a time span elapsed or a signal arrived). For a numeric argument, the current coroutine is scheduled in `*Next` for a point in time after that number of time units. For symbolic arguments, the current coroutine is queued into those symbol's event queues. In any case, control is passed to the next coroutine.
`(event 'sym 'exe)`
  Sends the signal `sym` to all coroutines waiting in that symbol's event queue. As a result, these coroutines are removed from the queue and appended to the `*Ready` queue, with the optional `exe` to be evaluated when resumed. The current coroutine continues to run.
`(wake 'sym 'exe)`
  Wakes up another coroutine `sym`, by appending it to the `*Ready` queue with the optional 'exe' to be evaluated when resumed. This means that if `sym` is currently waiting for a point in time in `*Next`, it is removed from that index (i.e. the pause is aborted). Also, if `sym` is waiting for signals, it is removed from those event queues. The current coroutine continues to run.

## Usage

A typical DES program will start some coroutines and let them perform their initial work until they need to pause.

That means, if a given operation in the simulation is supposed to take `cnt` time units, this coroutine calls `pause` with that number. Or, if it depends on some signals from another part of the program, it may call `pause` with those symbols. In any case - as it has nothing else to do - it goes to sleep.

When all of them wait for a time or signal, control is returned to the main program. All coroutines are now waiting in `*Next` or some signal event queue (or in `*Ready` if they just gave up control with `(pause)`).

The main program may now check `*Next` and perhaps `*Ready`. If both are empty, no further events can occur, and the program may terminate.

Otherwise, it calls `des` to continue with the next step(s).

At any time, a coroutine or the main program may call `wake`, for example to interrupt another coroutine and cause it to throw into some other context, or have that coroutine's `pause` return a special value by evaluating the `exe` argument.

## An Example

Let's use DES to demonstrate the well-known Dining Philosophers Problem.

Put the following code into a file "dining.l".

    # 07sep23 Software Lab. Alexander Burger
    # Dining Philosophers
    # pil dining.l -dining~main +

    (load "@lib/simul.l")

    (symbols 'dining 'simul 'pico)

    (local) (*ForkA *ForkB *ForkC *ForkD *ForkE now think)

    (de now (Str)
       (prinl (tim$ (* 60 *Time)) " " (co) " " Str) )

    (de think (Left Right)
       (loop
          (now "thinking")
          (pause (rand 180 240))  # 3 to 4 hours
          (now "hungry")
          (while (or (val Left) (val Right))
             (now "waiting")
             (pause Left Right) )
          (set Left (set Right (co)))
          (now "eating")
          (pause 20)  # 20 minutes
          (set Left (set Right NIL))
          (event Left)
          (event Right) ) )

    (local) main

    (de main ()
       (symbols '(dining simul pico))
       (co 'Aristotle
          (think '*ForkA '*ForkB) )
       (co 'Kant
          (think '*ForkB '*ForkC) )
       (co 'Spinoza
          (think '*ForkC '*ForkD) )
       (co 'Marx
          (think '*ForkD '*ForkE) )
       (co 'Russell
          (think '*ForkE '*ForkA) ) )

It uses five global variables `*ForkA` through `*ForkE` and five coroutines `Aristotle`, `Kant`, `Spinoza`, `Marx` and `Russell`. They all run the same function `think`, with their neighboring forks as `Left` and `Right` arguments.

In `think`, each philospher is first "thinking" for a random time between three and four hours. Then it gets "hungry", tries to pick up both forks, and - if at least one of the forks is in use - starts "waiting" for a left or right fork signal from another philosopher, and checks the forks again.

Now both forks are free. The philosopher puts himself into both (it could put in fact any non-`NIL` value), then is "eating" for 20 minutes, releases both forks by setting them to `NIL`, and sends a left and a right fork signal to the neighboring philosophers possibly waiting for the forks.

The simulation cannot deadlock, because both forks are picked up and released atomically, and because coroutines waiting for fork signals are always queued after the other waiting coroutines.

## Sample Run

    $ ./pil misc/dining.l -dining~main +
    00:00 Aristotle thinking
    00:00 Kant thinking
    00:00 Spinoza thinking
    00:00 Marx thinking
    00:00 Russell thinking
    dining: (more (stack))
    (Russell . 62)
    (Marx . 62)
    (Spinoza . 62)
    (Kant . 62)
    (Aristotle . 62)
    (T . 155)
    -> NIL
    dining: *Ready
    -> NIL
    dining: (idx '*Next)
    -> ((180 . Aristotle) (194 . Marx) (198 . Russell) (201 . Spinoza) (229 . Kant))
    dining: (des)
    03:00 Aristotle hungry
    03:00 Aristotle eating
    -> NIL
    dining: (des)
    03:14 Marx hungry
    03:14 Marx eating
    -> NIL
    dining: (des)
    03:18 Russell hungry
    03:18 Russell waiting
    -> NIL
    dining: (do 10 (des))
    03:20 Aristotle thinking
    03:20 Russell waiting
    03:21 Spinoza hungry
    03:21 Spinoza waiting
    03:34 Marx thinking
    03:34 Spinoza eating
    03:34 Russell eating
    03:49 Kant hungry
    03:49 Kant waiting
    03:54 Russell thinking
    03:54 Spinoza thinking
    03:54 Kant eating
    04:14 Kant thinking
    06:27 Aristotle hungry
    06:27 Aristotle eating
    06:47 Aristotle thinking
    06:47 Marx hungry
    06:47 Marx eating
    07:07 Marx thinking
    07:40 Russell hungry
    07:40 Russell eating
    -> NIL
    dining: