From 9f87eae10173427f95519672bc25eec57f550ca2 Mon Sep 17 00:00:00 2001 From: Vesa Karvonen Date: Thu, 18 May 2023 14:17:30 +0300 Subject: [PATCH] Sleeping barbers --- README.md | 265 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 265 insertions(+) diff --git a/README.md b/README.md index 09e78914..43b43df4 100644 --- a/README.md +++ b/README.md @@ -75,6 +75,7 @@ is distributed under the [ISC license](LICENSE.md). - [Programming with transactional data structures](#programming-with-transactional-data-structures) - [The dining philosophers problem](#the-dining-philosophers-problem) - [A transactional LRU cache](#a-transactional-lru-cache) + - [The sleeping barbers problem](#the-sleeping-barbers-problem) - [Programming with primitive operations](#programming-with-primitive-operations) - [Designing lock-free algorithms with k-CAS](#designing-lock-free-algorithms-with-k-cas) - [Understand performance](#understand-performance) @@ -1049,6 +1050,270 @@ val a_cache : (int, string) cache = As an exercise, implement an operation to `remove` associations from a cache and an operation to change the capacity of the cache. +#### The sleeping barbers problem + +The +[sleeping barber problem](https://en.wikipedia.org/wiki/Sleeping_barber_problem) +is another classic communication and synchronization problem. Let's write a +solution using **Kcas**. + +There are +[many ways to solve the problem](https://en.wikipedia.org/wiki/Sleeping_barber_problem#Solutions) +and, in particular, there are concise and subtle implementations using +semaphores or mutexes. Instead of transliterating a solution using semaphores, +our approach uses queues and other concurrent data structures. We also solve the +generalized problem with multiple barbers and we also implement a mechanism to +close the barbershop. In addition, we abstract the concept of a barbershop, +where barbers and customers interact. All of this makes our solution longer than +the well known semaphore based solution. On the other hand, one might argue that +our solution is a more direct transliteration of the problem. Our solution also +avoids the starvation problem by using queues. + +Let's begin by abstracting customer + +```ocaml +type customer = { + notify_hair_has_been_cut : 'x.xt:'x Xt.t -> unit; +} +``` + +and barber + +```ocaml +type barber = { + wake_up : 'x.xt:'x Xt.t -> customer -> unit; +} +``` + +actors. The idea is that barbers notify customers after finishing their haircut +and, adhering to the problem description, customers wake up sleeping barbers. + +A barbershop consists of any number of barbers and waiting customers and can be +marked as closed: + +```ocaml +type barbershop = { + sleeping_barbers : barber Queue.t; + waiting_customers : customer Queue.t; + is_closed : bool Loc.t; +} +``` + +The barbershop constructor does not limit the number of barbers, which are +assumed to bring their own chairs, but does require a specification of the +number of waiting room chairs for customers: + +```ocaml +# let barbershop ~num_waiting_chairs = + let sleeping_barbers = Queue.create () + and waiting_customers = Queue.create ~capacity:num_waiting_chairs () + and is_closed = Loc.make false in + { sleeping_barbers; waiting_customers; is_closed } +val barbershop : num_waiting_chairs:int -> barbershop = +``` + +Although the `barbershop` type is not abstract, we treat it as such, so we +provide a transactional predicate to check whether the barbershop is closed or +not: + +```ocaml +# let is_closed ~xt bs = Xt.get ~xt bs.is_closed +val is_closed : xt:'a Xt.t -> barbershop -> bool = +``` + +To `close` a barbershop we set the `is_closed` location to `true` and clear both +the sleeping barbers and waiting customers queues: + +```ocaml +# let close ~xt bs = + Xt.set ~xt bs.is_closed true; + Queue.Xt.clear ~xt bs.sleeping_barbers; + Queue.Xt.clear ~xt bs.waiting_customers +val close : xt:'a Xt.t -> barbershop -> unit = +``` + +A barber can try to get a customer sitting on a waiting room chair: + +```ocaml +# let get_sitting_customer_opt ~xt bs = + Queue.Xt.take_opt ~xt bs.waiting_customers +val get_sitting_customer_opt : xt:'a Xt.t -> barbershop -> customer option = + +``` + +Or may go to sleep on the barber's own chair: + +```ocaml +# let sleep ~xt bs barber = + if not (is_closed ~xt bs) then + Queue.Xt.add ~xt barber bs.sleeping_barbers +val sleep : xt:'a Xt.t -> barbershop -> barber -> unit = +``` + +Note that the `sleep` transaction uses the `is_closed` predicate. Barbers, as +well as customers, must leave the shop in case it is closed. + +A customer can try to find a sleeping barber: + +```ocaml +# let get_sleeping_barber_opt ~xt bs = + Queue.Xt.take_opt ~xt bs.sleeping_barbers +val get_sleeping_barber_opt : xt:'a Xt.t -> barbershop -> barber option = + +``` + +Or sit on a waiting room chair: + +```ocaml +# let try_sitting ~xt bs customer = + not (is_closed ~xt bs) && + Queue.Xt.try_add ~xt customer bs.waiting_customers +val try_sitting : xt:'a Xt.t -> barbershop -> customer -> bool = +``` + +The above `try_sitting` transaction is non-blocking. In case the +`waiting_customers` queue is full, it will return `false`. With the `customer` +actor implementation we'll look at shortly this would mean that customers would +busy-wait, which works, but potentially wastes energy. Here is a blocking +version of `try_sitting`: + +```ocaml +# let try_sitting ~xt bs customer = + not (is_closed ~xt bs) && + begin + Queue.Xt.add ~xt customer bs.waiting_customers; + true + end +val try_sitting : xt:'a Xt.t -> barbershop -> customer -> bool = +``` + +Both of the above `try_sitting` transactions work with the `customer` actor +we'll see shortly, but with the latter blocking version we avoid busy-wait. + +The above constitutes the barbershop abstraction which is a kind of passive +concurrent data structure. Let's then implement the active participants of the +problem. + +A customer tries to get a haircut. When a customer enter the barbershop he first +tries to find a sleeping barber. If none is available, the customer then tries +to sit on a waiting room chair. If both fail, then the customer has no option +except to retry. Otherwise the customer waits to get a haircut. If the shop is +closed, the customer exits. Here is the `customer` actor: + +```ocaml +# let customer shop cuts = + let clean = Mvar.create None in + let self = { notify_hair_has_been_cut = Mvar.Xt.put clean true } in + while not (Xt.commit { tx = is_closed shop }) do + let get_barber_opt ~xt = + match get_sleeping_barber_opt ~xt shop with + | None -> + try_sitting ~xt shop self + | Some barber -> + barber.wake_up ~xt self; + true + in + if Xt.commit { tx = get_barber_opt } then + let try_await_haircut ~xt = + not (is_closed ~xt shop) && + Mvar.Xt.take ~xt clean + in + if Xt.commit { tx = try_await_haircut } then + Loc.incr cuts + done +val customer : barbershop -> int Loc.t -> unit = +``` + +A barber tries to get a customer to give a haircut. A barber first looks for a +customer from the waiting room. If none is available, the barber goes to sleep +waiting for a wakeup from a customer. After obtaining a customer in either way, +the barber gives a haircut to the customer. Otherwise the shop must be closed +and the barber exits. Here is the `barber` actor: + +```ocaml +# let barber shop cuts = + let customer = Mvar.create None in + let self = { wake_up = Mvar.Xt.put customer } in + while not (Xt.commit { tx = is_closed shop }) do + let cut customer = + Xt.commit { tx = customer.notify_hair_has_been_cut }; + Loc.incr cuts + in + let get_customer_opt ~xt = + match get_sitting_customer_opt ~xt shop with + | Some _ as some -> some + | None -> + sleep ~xt shop self; + None + in + match Xt.commit { tx = get_customer_opt } with + | Some customer -> cut customer + | None -> + let await_wakeup_opt ~xt = + if is_closed ~xt shop then None + else Some (Mvar.Xt.take ~xt customer) + in + match Xt.commit { tx = await_wakeup_opt } with + | Some customer -> cut customer + | None -> () + done +val barber : barbershop -> int Loc.t -> unit = +``` + +To run the problem, a barbershop is created with given number of waiting room +chairs, is populated by given number of barbers, and a given number of customers +are spawned. Once each barber has given and each customer has received a given +number of haircuts the shop is closed. This termination condition seeks to +demonstrate that no actor is starved. Here is the `sleeping_barbers` setup: + +```ocaml +# let sleeping_barbers ~barbers + ~num_waiting_chairs + ~customers + ~cuts_per_actor = + assert (0 < barbers + && 0 <= num_waiting_chairs + && 0 <= customers + && 0 <= cuts_per_actor); + let shop = barbershop ~num_waiting_chairs in + let barbers = Array.init barbers @@ fun _ -> + let cuts = Loc.make 0 in + (cuts, Domain.spawn @@ (fun () -> barber shop cuts)) + and customers = Array.init customers @@ fun _ -> + let cuts = Loc.make 0 in + (cuts, Domain.spawn @@ (fun () -> customer shop cuts)) + in + let agents = Array.append barbers customers in + while agents + |> Array.map fst + |> Array.exists @@ fun c -> + Loc.get c < cuts_per_actor do + Domain.cpu_relax () + done; + Xt.commit { tx = close shop }; + agents + |> Array.map snd + |> Array.iter Domain.join +val sleeping_barbers : + barbers:int -> + num_waiting_chairs:int -> customers:int -> cuts_per_actor:int -> unit = + +``` + +Finally, let's try our solution: + +```ocaml +# sleeping_barbers ~barbers:2 + ~num_waiting_chairs:1 + ~customers:4 + ~cuts_per_actor:10 +- : unit = () +``` + +Like mentioned in the beginning, this is not the most concise solution of the +sleeping barbers problem, but hopefully this solution can be understood +relatively easily with respect to the problem description. + ### Programming with primitive operations In addition to the transactional interface, **Kcas** also provides the