= Solution
The capacity and quality targets alone do not determine flow counts: the per-flow traffic statistics must also be supplied. The following explicit model gives a computable sufficient region, with genuine upper bounds on both loss fractions.
Measure <queue workload> and buffer size in bits. Denote capacity by $C$, shared buffer size by $B$, voice delay limit by $D$, target voice loss by $\ell_v$, and target data loss by $\ell_d$, with $0<\ell_v,\ell_d<1$. Let there be $n_v$ voice flows and $n_d$ data flows. Model each class-$j$ flow, $j\in\{v,d\}$, by a stationary <Compound Poisson process> with packet rate $\nu_j$ and positive <independent> packet sizes $S_j$, and assume <independence> across flows and marks. Use a work-conserving preemptive-resume <priority queue with a shared buffer>, with voice priority and <first come first served> within each class. This preemptive or fluid approximation makes the predicted voice waiting time exactly $V/C$, where $V$ is the remaining voice <queue workload> just before arrival. Assume packet sizes are bounded by a known $s_{\max}<B$ and interpret the buffer gate as a packet-fit test; rejecting packets which do not fit is the packet version of the full-buffer rule.
For one flow the <Compound Poisson process> formula gives
$$
\Lambda_j(\theta)=\nu_j(\mathbb E e^{\theta S_j}-1),\qquad
\boxed{a_j(\theta)=\frac{\nu_j(\mathbb E e^{\theta S_j}-1)}{\theta}.}
$$
For fixed-size packets of size $s_j$, substitute $e^{\theta s_j}$. Estimate the packet rate and size law from measurements or a declared traffic contract. Also require the strict stability inequality
$$
n_v\nu_v\mathbb E S_v+n_d\nu_d\mathbb E S_d<C.
$$
Define $B_0=B-s_{\max}>0$ and $K=CD$. Couple the switch with an unthinned infinite-buffer aggregate <queue> and an unthinned infinite-buffer voice-only <queue>, both driven by the same offered packets and both served at rate $C$. Under the preemptive <service discipline>, dropping arrivals can only decrease both the total <queue workload> and the voice <queue workload>. Thus total switch <queue workload> $Q$ and voice <queue workload> $V$ satisfy $Q\leq W_T$ and $V\leq W_V$ in the stationary coupling. A packet-fit loss implies $Q>B-S_j\geq B_0$, and a voice-delay rejection implies $V\geq K$.
Apply the <continuous-time exponential workload bound> to the two comparison <queues>. For any positive $\theta_T,\theta_V$ satisfying
$$
n_v a_v(\theta_T)+n_d a_d(\theta_T)\leq C,\qquad
n_v a_v(\theta_V)\leq C,
$$
the stationary loss-event <probabilities> obey
$$
\boxed{p_d\leq e^{-\theta_T B_0},\qquad
p_v\leq e^{-\theta_T B_0}+e^{-\theta_V K}.}
$$
The second inequality is a <union bound>: voice can be lost either at the shared buffer or at its delay gate. Data congestion therefore contributes to voice loss despite its lower service priority. <Poisson arrivals see time averages> applies to each offered packet stream, whose future arrivals are <independent> of the prearrival state; the stationary event bounds are consequently bounds on the offered-packet loss fractions. Voice packets that are admitted have <queueing delay> below $D$, because later voice packets join behind them and data work cannot delay them in this model.
To turn the bounds into flow counts, allocate loss budgets
$$
0<\eta_B<\min(\ell_d,\ell_v),\qquad
\eta_V=\ell_v-\eta_B,\qquad
\theta_T=\frac{\log(1/\eta_B)}{B_0},\quad
\theta_V=\frac{\log(1/\eta_V)}{CD}.
$$
For example, $\eta_B=\min(\ell_d,\ell_v/2)$ and $\eta_V=\ell_v-\eta_B$ also work; equality with $\ell_d$ is harmless. The required sufficient <effective-bandwidth admission region with a voice delay gate> is
$$
\boxed{\begin{gathered}
n_v a_v(\theta_V)\leq C,\\
n_v a_v(\theta_T)+n_d a_d(\theta_T)\leq C,\\
n_v\nu_v\mathbb E S_v+n_d\nu_d\mathbb E S_d<C,\qquad
n_v,n_d\in\mathbb Z_{\geq0}.
\end{gathered}}
$$
It ensures $p_d\leq\ell_d$ and $p_v\leq\ell_v$. A simple enumeration is
$$
0\leq n_v\leq\left\lfloor\frac C{a_v(\theta_V)}\right\rfloor,\qquad
0\leq n_d\leq
\left\lfloor\frac{C-n_v a_v(\theta_T)}{a_d(\theta_T)}\right\rfloor,
$$
discarding negative bounds and pairs failing strict mean-load stability. The formulas assume positive-rate nonzero-size flows. Optimize a chosen revenue or flow-count objective over these integer pairs. Searching over the budget split $\eta_B$ can enlarge the sufficient region. For a bit-fluid buffer gate with no packet-fit issue, $B_0$ can be replaced by $B$.
Real nonpreemptive packet service needs an additional residual-service allowance or an explicit priority <queue workload> analysis: a voice packet may have to wait for the data packet already in service. Burst-correlated voice sources also require richer descriptors, such as measured finite-time <effective bandwidths> $\alpha_j(\theta,t)$ or a Markov-modulated source model. For such inputs, additivity still holds for <independent> flows, but the independent-increment supermartingale bound is not automatic; use a valid sample-path <large deviation principle> or a model-specific overflow bound, with prefactors or a safety margin when using asymptotics. If packet arrivals do not form a <Poisson process>, loss fractions must be assessed at arrival epochs rather than inferred solely from time-average <queue workload> <probabilities>. These qualifications explain both how to calculate an admission region from specified traffic statistics and why the five switch/QoS parameters by themselves cannot supply a numerical answer.
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