dead simple pure-bash "job scheduler" with configurable number of background processes

run-async.sh

#!/bin/bash

run-async() {
    local joblist=($(jobs -p))
    while (( ${#joblist[*]} >= 4 )); do # set 4 to the maximum number of jobs you want
        sleep 0.1
        joblist=($(jobs -p))
    done
    if [[ $# -eq 0 ]]; then # start shell with provided input if no arguments
        local code="$(</dev/stdin)"
        bash -c "$code" &
    else # otherwise launch arguments as command
        "$@" &
    fi
}

# example (arguments)
for i in {1..8}; do
    run-async bash -c "echo starting $i; sleep 3; echo stopping $i"
done

# example (stdin)
for i in {9..16}; do
    run-async <<-EOF
        echo starting $i
        sleep 3
        echo stopping $i"
EOF
done

wait