Israeli Queues

A queue is a data structure that holds up elements for a brief period of time until a peripheral processing system is ready to process them. The most common implementation of a queue is a FIFO queue - First In First Out - that evicts the element that was inserted the first i.e. it evicts the one that has spent the most time in the queue. There are other variations of Queues one of which is called Priority Queue.

In Priority Queue, every element is associated with a priority, usually provided by the user during enqueueing; This associated priority is used during eviction where the element with the highest priority is evicted first during dequeuing.

In this essay, we take a detailed look into a variation of Priority Queue, fondly called Israeli Queues, where the priority of the element is defined by the affinity of it with one of its "friends" in the queue. Israeli Queues were first introduced in the paper Polling with batch service by Boxma, O. J., Wal, van der, J., & Yechiali, U in the year 2007.

Israeli Queues

Queues in Israel are usually unorganized, due to which people tend to find their friends, who are already waiting, and instead of adhering to the usual protocol of joining at the back end, they cut through and directly join their friends. Israeli Queues mimic this behavior and hence get this punny name.

Israeli Queues are a variation of Priority Queues where instead of associating priority with the element to be enqueued, the priority is implicitly derived using the "friend" element and it joins right at the back end of the group that the friend belongs to. The function signature of the enqueue operation is as shown below, while other operations like dequeue and peek remains fairly similar.

// Enqueues the element `e`, a friend of element `f`,
// into the queue `q`.
void enqueue(israeli_queue * q, element * e, element * f);

How could this help?

Every Data Structures is designed to solve a niche use case efficiently and Israeli Queues are no different as they prove to be super-efficient where one could batch and process similar elements or where the set-up cost for a task is high.

Consider a system where a queue is used to hold up heterogeneous tasks and there is a single machine taking care of processing. Now if some of these tasks are similar and have a high set-up or preparation cost, for example downloading large metafiles, or spinning up a parallel infrastructure, or even setting up persistent connections with device farms, queuing them closer and processing them sequentially or in batch helps in reducing redundant processing and computation by promoting reuse.

Issue of starvation

By enqueuing elements in between Israeli Queues reduces redundant processing, but by doing that it makes itself vulnerable to the classical case of starvation. Elements stuck at the rear end of the list could potentially starve for longer durations if elements having "friends" in the queue keep coming in at high frequency.

The original implementation of Israeli Queues suggests batch processing where instead of processing tasks one at a time, it processes a batch (a group of friends) in one go. This proves to be super-handy when the time required to processes a single task is much lower than the set-up cost for it.

Implementation Guidelines

The best way to implement Israeli Queues is by using a Doubly Linked List with a bunch of pointers pointing to the head and tail of groups within it. Insertion to an existing group happens at the tail of it while if the element has no friend element, then it goes at the tail end of the list and forms its own group.

A constraint that could be added during implementation is that the friend element should always be the leader (head) element of the group. Details of the implementation could be tweaked so long the core concept remains unaltered.

The original use case of Israeli Queues

Israeli Queues were the outcome of a problem statement dealing with Polling Systems. Polling System usually contains N queues Q1, Q2, ..., Qn where the processing unit visits each queue in cyclic order processing one element at a time i.e. Q1, Q2, ..., Qn, Q1, Q2, ..., Qn, etc.

When the server attends a queue instead of processing just one element from it, it processes the entire batch present in the queue utilizing the setup-cost efficiently assuming that time to process an element from a queue is much lesser than the set-up cost.


Arpit Bhayani

Arpit's Newsletter

CS newsletter for the curious engineers

❤️ by 30000+ readers

If you like what you read subscribe you can always subscribe to my newsletter and get the post delivered straight to your inbox. I write essays on various engineering topics and share it through my weekly newsletter.

Other essays that you might like

2Q Cache Management Algorithm

1705 reads 2020-11-29

LRU is one of the most widely used cache eviction algorithms suffers from a bunch of limitations especially when used fo...

Morris's Algorithm for Approximate Counting

2120 reads 2020-08-02

Morris' Algorithm counts a large number of events using a very small space O(log log n). The algorithm uses probabilisti...

Phi φ Accrual Failure Detection

478 reads 2020-07-12

Phi φ Accrual Failure Detection algorithm, unlike conventional algorithms, is an adaptive failure detection algorithm th...

Copy-on-Write Semantics

559 reads 2020-05-03

Copy-on-write is used to model Time Travel, build databases with no locks, and makes the fork system call super-efficien...

Be a better engineer

A set of courses designed to make you a better engineer and excel at your career; no-fluff, pure engineering.

Paid Courses

System Design Masterclass

A masterclass that helps you become great at designing scalable, fault-tolerant, and highly available systems.

1000+ learners

Details →

Redis Internals

Learn internals of Redis by re-implementing some of the core features in Golang.

46+ learners

Details →

Free Courses

Designing Microservices

A free playlist to help you understand Microservices and their high-level patterns in depth.

106+ learners

Details →

GitHub Outage Dissections

A free playlist to help you learn core engineering from outages that happened at GitHub.

251+ learners

Details →

Hash Table Internals

A free playlist to help you understand the internal workings and construction of Hash Tables.

427+ learners

Details →

BitTorrent Internals

A free playlist to help you understand the algorithms and strategies that power P2P networks and BitTorrent.

192+ learners

Details →

Topics I talk about

Being a passionate engineer, I love to talk about a wide range of topics, but these are my personal favourites.