Design a Low-Latency Bounded Queue and Size Its Capacity

Problem: Design a Low-Latency Bounded Queue and Size Its Capacity Design a bounded in-memory queue for a latency-sensitive data path. Producers continuously write messages and consumers read them. The goal is to minimize enqueue/dequeue latency and avoid dynamic allocation during normal operation. Design Requirements State which concurrency model must be established first: SPSC, MPSC, SPMC, or MPMC. For the SPSC (single-producer, single-consumer) case, implement or describe a fixed-capacity ring buffer that: provides try_push(item), which fails immediately when full; provides try_pop(), which fails immediately when empty; uses neither mutexes nor dynamic allocation on the normal data path; handles head/tail wraparound correctly; explains the required C++ memory ordering and how to avoid false sharing between producer and consumer state. Explain what must change for MPSC or MPMC, and why a naive SPSC implementation cannot be reused directly. Derive a capacity-sizing method. Let: B be the maximum burst size; λ be the sustained producer rate after the burst, in messages/second; μ be a conservative lower bound on consumer throughput, in messages/second; T_pause be the longest consumer pause; T be the load window during which no loss is required. Give the capacity requirement for both λ > μ and λ <= μ. Explain why a finite queue alone cannot guarantee no overflow when λ > μ persists indefinitely, and describe the safety margin that should be added. Example For B = 10,000, λ = 800,000/s, μ = 1,000,000/s, and T_pause = 5ms, the lower bound on backlog caused by the burst and consumer pause alone is: 10,000 + 800,000 × 0.005 = 14,000 The real capacity should additionally include headroom for measurement error, scheduling jitter, and recovery behavior, and is commonly rounded up to a ring-buffer-friendly capacity.