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First of all, What is the difference between mutex & semaphore.
Binary semaphore is also called MUTEX as per their values but their purposes are different..
Semaphore is used for signalling purpose. A thread waiting for a semaphore might be signalled by the other thread.
Mutex is used for Blocking purpose.
Mutex is used to provide synchronization on same block of code.
An ownership kind of thing is attached with a MUTEX. The lock is released by the object which has acquired it.
While semaphore is used to control the access to finite number of resources.

Since, here is only queue,
Hence, i feel that MUTEX would be a better choice.

As the question clearly states "one or many process try to access the queue"?

This support can be provided by Semaphore as it allows multiple process to enter and read the contents. And we can use "Mutex" which is kind of binary semaphore for writing.
Once the "Semaphore" count is zero one of the process can claim the "mutex" and write.

Another question arises of "concurrency" which can be handled different ways check out linux RCU (Read-Copy-Update) on similar lines.

Mutex can be modelled using a binary Semaphore.

So this question is pointless.

I would prefer other contending process to sleep, and hence I will use a semaphore.

Semaphore. Because Mutex can only be used among threads. Semaphores are for inter-process communication

Semaphore

When multiple processes are accessong a shared data, then, semaphore is the best way.because mutex has a ownership attached to it and a process taking the ownership of lock can only release it.