Module Priority_queue

Timing wheel is implemented as a priority queue in which the keys are non-negative integers corresponding to the intervals of time. The priority queue is unlike a typical priority queue in that rather than having a "delete min" operation, it has a nondecreasing minimum allowed key, which corresponds to the current time, and an increase_min_allowed_key operation, which implements advance_clock. increase_min_allowed_key as a side effect removes all elements from the timing wheel whose key is smaller than the new minimum, which implements firing the alarms whose time has expired.

Adding elements to and removing elements from a timing wheel takes constant time, unlike a heap-based priority queue which takes log(N), where N is the number of elements in the heap. increase_min_allowed_key takes time proportional to the amount of increase in the min-allowed key, as compared to log(N) for a heap. It is these performance differences that motivate the existence of timing wheels and make them a good choice for maintaing a set of alarms. With a timing wheel, one can support any number of alarms paying constant overhead per alarm, while paying a small constant overhead per unit of time passed.

As the minimum allowed key increases, the timing wheel does a lazy radix sort of the element keys, with level 0 handling the least significant b_0 bits in a key, and each subsequent level i handling the next most significant b_i bits. The levels hold increasingly larger ranges of keys, where the union of all the levels can hold any key from min_allowed_key t to max_allowed_key t. When a key is added to the timing wheel, it is added at the lowest possible level that can store the key. As the minimum allowed key increases, timing-wheel elements move down levels until they reach level 0, and then are eventually removed.


type 'a t
val sexp_of_t : ('a -> Sexplib.Sexp.t) -> 'a t -> Sexplib.Sexp.t
type 'a priority_queue = 'a t
module Elt : sig .. end
include Invariant.S1 with type 'a t := 'a t
type 'a t
val invariant : 'a Invariant_intf.inv -> 'a t Invariant_intf.inv
val create : ?level_bits:Level_bits.t -> unit -> 'a t

create ?level_bits () creates a new empty timing wheel, t, with length t = 0 and min_allowed_key t = 0.

val length : _ t -> int

length t returns the number of elements in the timing wheel.

val is_empty : _ t -> bool

is_empty t is length t = 0

val min_allowed_key : _ t -> Key.t

min_allowed_key t is the minimum key that can be stored in t. This only indicates the possibility; there need not be an element elt in t with Elt.key elt = min_allowed_key t. This is not the same as the "min_key" operation in a typical priority queue.

min_allowed_key t can increase over time, via calls to increase_min_allowed_key. It is guaranteed that min_allowed_key t <= Key.max_representable.

val max_allowed_key : _ t -> Key.t

max_allowed_key t is the maximum allowed key that can be stored in t. As min_allowed_key increases, so does max_allowed_key; however it is not the case that max_allowed_key t - min_allowed_key t is a constant. It is guaranteed that max_allowed_key t >= min (Key.max_representable, min_allowed_key t + 2^B - 1, where B is the sum of the b_i in level_bits. It is also guaranteed that max_allowed_key t <= Key.max_representable.

val min_elt : 'a t -> 'a Elt.t option

min_elt t returns an element in t that has the minimum key, if t is nonempty. min_elt takes time proportional to the size of the timing-wheel data structure in the worst case. It is implemented via a linear search.

min_key t returns the key of min_elt t, if any.

val min_key : _ t -> Key.t option
val add : 'a t -> key:Key.t -> 'a -> 'a Elt.t

add t ~key value adds a new value to t and returns an element that can later be supplied to remove the element from t. add raises if key < min_allowed_key t || key > max_allowed_key t.

val remove : 'a t -> 'a Elt.t -> unit

remove t elt removes elt from t. It is an error if elt is not currently in t, and this error may or may not be detected.

val change_key : 'a t -> 'a Elt.t -> key:Key.t -> unit

change_key t elt ~key changes the key of elt to key. change_key raises if not (mem t elt) || key < min_allowed_key t || key > max_allowed_key t.

val clear : _ t -> unit

clear t removes all elts from t.

val mem : 'a t -> 'a Elt.t -> bool
val increase_min_allowed_key : 'a t -> key:Key.t -> handle_removed:('a Elt.t -> unit) -> unit

increase_min_allowed_key t ~key ~handle_removed increases the minimum allowed key in t to key, and removes all elements with keys less than key, applying handle_removed to each element that is removed. If key <= min_allowed_key t, then increase_min_allowed_key does nothing. Otherwise, if increase_min_allowed_key returns successfully, min_allowed_key t = key.

increase_min_allowed_key raises if key > Key.max_representable.

increase_min_allowed_key takes time proportional to key - min_allowed_key t, although possibly less time.

Behavior is unspecified if handle_removed accesses t in any way other than Elt functions.

val iter : 'a t -> f:('a Elt.t -> unit) -> unit